new linear codes from 260109

• binary: 4 improvements + 4 derived
• ternary: 2 improvements + 4 derived
• q=4 : 2 optimal + 14 improvements + 32 derived
• q=5:
• q=7:2 improvement
• q=8: 4 improvements + 3 derived
• q=9:

binary q=2

q=2 k=13 n=154 d=68

(computed with a program of Johannes Zwanzger)
( link )

generator matrix:
0000011111111110000000111111110000011111111110000000001111110000000001111110000000000011110000000001111110000000001111110000000111111110000000000011110000
0000100011111110000011000011110011100000111110000111110001110000111110001110000000111100110000001110000010000001110001110001111000000110000011111100001111
0000000100000110001101011101110000100011000010011000110010110000111110001110001111001111110011110010001110001110010111110110011000011000011100111100111101
0011100100001000110111000101110101000001001110100011110110110011011110110110010111111101010100010110001101110010101010001001101001111110100101000001010111
0100111100111010110100111001110001000111000111000111001111010111101110110010100011110100000001110000010110010110011010011000100011101001011101001110101000
0001001000010001110000101110111011111110011110100000000010011101111110111011010000011010010111101011111110010111101011100000011100110011101100011110010111
0011000011110001010110110011110010111000000110001001111000100111100111111001101011011100110100010110001100110010011100110000011011001100000110010100110101
0010110111100001010001111011010100011001110111001101000011010000001000110101100001000101101010100000100000001000101100100110011000011001100111001100111101
0110010100100100100010101001101001001110000011011111110010011010001011010001111001110111001000011010110000001101010101111110001001100000011101011011110101
0101011101011001010010000101100001111001001111000110011100110101001101111001100111010111011000111111100000101111111100011010001111101110110000001011011001
0001101111101000010100100011011101101011001001110000011101011101001000000000100011001000110010110101101100001101011010001101010000010100111010000010010101
0111011111100011101000100010010101101000100010101000100110101111111001011001100010111110111001001111110111101010111100000110100111111100110101100000010011
1101111110010011111010000110100010100101001100111100000010010110110111100111000001001001000010010000111100010000111010100000100100101001001011111000101001
mindist=68
weight enumerator=1 [0]  1028 [68]  1060 [70]  262 [72]  2116 [76]  1316 [78]  204 [80]  
1356 [84]  652 [86]  42 [88]  108 [92]  44 [94]  3 [96]  

q=2 k=13 n=157 d=70

(computed with a program of Johannes Zwanzger)
( link )

generator matrix:
0000011111111110000000111111110000011111111110000000001111110000000001111110000000000011110000000001111110000000001111110000000111111110000000000011110110000
0000100011111110000011000011110011100000111110000111110001110000111110001110000000111100110000001110000010000001110001110001111000000110000011111100001001110
0000000100000110001101011101110000100011000010011000110010110000111110001110001111001111110011110010001110001110010111110110011000011000011100111100111101011
0011100100001000110111000101110101000001001110100011110110110011011110110110010111111101010100010110001101110010101010001001101001111110100101000001010001110
0100111100111010110100111001110001000111000111000111001111010111101110110010100011110100000001110000010110010110011010011000100011101001011101001110101110000
0001001000010001110000101110111011111110011110100000000010011101111110111011010000011010010111101011111110010111101011100000011100110011101100011110010111110
0011000011110001010110110011110010111000000110001001111000100111100111111001101011011100110100010110001100110010011100110000011011001100000110010100110101011
0010110111100001010001111011010100011001110111001101000011010000001000110101100001000101101010100000100000001000101100100110011000011001100111001100111101011
0110010100100100100010101001101001001110000011011111110010011010001011010001111001110111001000011010110000001101010101111110001001100000011101011011110101011
0101011101011001010010000101100001111001001111000110011100110101001101111001100111010111011000111111100000101111111100011010001111101110110000001011011110010
0001101111101000010100100011011101101011001001110000011101011101001000000000100011001000110010110101101100001101011010001101010000010100111010000010010011011
0111011111100011101000100010010101101000100010101000100110101111111001011001100010111110111001001111110111101010111100000110100111111100110101100000010100111
1101111110010011111010000110100010100101001100111100000010010110110111100111000001001001000010010000111100010000111010100000100100101001001011111000101000010
mindist=70
weight enumerator=1 [0]  1558 [70]  792 [72]  2774 [78]  862 [80]  1682 [86]  368 [88]  130
 [94]  25 [96]  

q=2 k=16 n=161 d=66

(extension of a code with automorphisms)
( link )

generator matrix:
00000000000000000001111111111111111111100000000000000000001111111111111111111100000000000000000001111111111111111111100000000000000000000000111111111111111100000
00000000111111111110000000000111111111100000000000001111110000000000001111111100000001111111111110000000000000011111100000000000011111111111000000111111111101111
00011111000000001110001111111000111111100000011111110011110000001111110000111100011110000000111110000011111111100011100000001111100000111111000111000111111101110
00100011000001110010110000111001000001101111100000111111110000110000110001000111100110111111011110011100001111101101101111110000000011000011001001001000011100001
11001100000110111111110011011111001110100001100111010100110001110001111110011101111011000111000110100101110001110001110000110001111100000101111001011001100010101
00000101001010011110011100101010000111110000101000000001011111010010011111000100001010011011101010100110010010110000100011000110101111000101111001101111100010110
01111110110011010101110111110101110011001111100111110111010011000100010011001110101001011000110001011111100000000110100101110010001100000111110010011010100101100
10111101111011101000000100111010110101110110101011000100001100111101000111100100011001101011011010111000000110101101101100001110010100011110110010101100001100011
10111101011100101001000100000101000101000110100101101010111111100100110100011111000100001001111111101000001000100111011000111000110001000001010111001001100101111
00110101101001111110000001001110010111001010111011111101101110110010001001010100000111010011101011111110001100111101111111010111001001100001011100101001111100010
10101100001010100011001000100010101000001011011010010101000100100001001110101000110100110101110001111000101010001111110010011110010100011010011111101001011011010
00100100000001110001101001011010000011100001100010010100011111100011100000001111001100101101000000010010010111001010010110000101101001001011111100000110001100011
11010011110011001110011010011111000110000100010000011110111110001110101010100011011100000110011010111100010010100001001001100001000001101010100100001111000001100
01001000010001110101101011001110001101100111101010001100100001111000010100111110110010010101001101110100011011101000011011001111111110000010011001110000000100001
01010001110100111011110000011111011100101001000001101111111110111011001000110101101001000000111101001001111010001011010010000110001001110110100001010110111001100
11000110111010111101010110110110100100001000110111000011010101101101101000000000111010110011000100000101110000110100101101101010110111000101111011111011010101110
mindist=66
weight enumerator=1 [0]  975 [66]  1449 [68]  2184 [70]  4095 [72]  4368 [74]  5616 [76]  
7683 [78]  8347 [80]  7725 [82]  7020 [84]  6279 [86]  4017 [88]  2613
 [90]  1716 [92]  741 [94]  468 [96]  156 [98]  39 [100]  39 [102]  3 [106
]  2 [118]  

q=2 k=16 n=164 d=68

(extension of a code with automorphisms)
( link )

generator matrix:
00000000000000000001111111111111111111100000000000000000001111111111111111111100000000000000011111111111111111111111100000000000000011111111111111111111111100000000
00000000111111111110000000000111111111100000000001111111110000000000001111111100000000011111100000000000011111111111100000001111111100000000000000111111111101110111
00011111000000001110001111111000111111100000001110000011110000000111110001111100001111100111100000011111100000011111100000110000011100000001111111000001111101111000
00100011000001110010110000111001000001100001110110001101110000001000110000011100010111111001100111100000000011100011100011000000100000111110001111000110000100001111
11001100000110111111110011011111001110100010110010010010110001110001010110101111111011111000111001100111111100000101101101010001001111001110010011111010011010100011
00000101001010011110011100101010000111101110111010010101010110010001111001010101100101101111001010111001101111111100110011110000100101010000110001001110101010110010
01111110110011010101110111110101110011010110011100000101111010110010011111100100011100011011111000000000110111101001000100100110100111100010111111111010101001100110
10111101111011101000000100111010110101110101001000010011110001100110111010001100100000111110000011001010010000000000100010101111111100011110000011001011000100010001
10111101011100101001000100000101000101000001010000011011100011101000001101110111001001000110000110111011110001110000001010101000000000010010100000001001000101110111
00110101101001111110000001001110010111001101001100011101000001111010001011010111000111001111000101010000110000011101111011100001011110110110101100011110100100011110
10101100001010100011001000100010101000010011010110100000000111011000110101010001100100000000001100010100110110000011011001011000011010110010100111010110111011010100
00100100000001110001101001011010000011100101101100101000110000111111100001001110011100000111111100000100000100011010001001101000001101011011101000010111101100010001
11010011110011001110011010011111000110010000001110111010001011001111010000110000011100101101100110101110000100010101000000111011111000010110001000111000101101100110
01001000010001110101101011001110001101110011011111101101110100000111100011101110110000110000010010011010000001110101001000000110101010110011110010111010001100001111
01010001110100111011110000011111011100110001100010110101001110110010111000001001101011010010101110011011001010000010010011011100001111101100101001100011111001100110
11000110111010111101010110110110100100001101101111001110000010101111010001010101111110011100011101101001011100111101101001111100010011111110110000100001011101111000
mindist=68
weight enumerator=1 [0]  1287 [68]  1137 [69]  2613 [72]  3666 [73]  4719 [76]  5265 [77
]  7606 [80]  8424 [81]  7296 [84]  7449 [85]  5928 [88]  4368 [89]  2418
 [92]  1911 [93]  741 [96]  468 [97]  117 [100]  78 [101]  39 [104]  3
 [108]  2 [121]  

ternary q=3

q=3 k=9 n=50 d=27

(extension of a code with  automorphisms)
( link )

generator matrix:
00000000111111111111111111111111111111110000000001
00000001011122220111222200011122000011220111111111
00000010101212221022112212200101001202011011122211
00000100210211222112021210122010022001101202212211
00001000221201121222120101001212201100202221210111
00010000222210112121221021210100010220101121021111
00100000222121012220112110012021120100021212121011
01000000122122102211201202100211210012002222102211
10000000112022211202212121121000102020012120211211
mindist=27
weight enumerator=1 [0]  1648 [27]  3976 [30]  6572 [33]  5704 [36]  1584 [39]  196 [42]  
2 [48]  
This is a self-orthogonal code

q=3 k=9 n=200 d=123

(extension of a code with  automorphisms)
( link )

generator matrix:
00000011111111111111111111111111000000000000111111111111111111110000000000000001111111111111111100000000011111111111111111111111000000000111111111111111111111110000000000001111111111111111111101110111
01111100000000111111111112222222000001111111000000011111112222220000011111111110000111111122222200001111100000111111111112222222001111111000000011111112222222220000111111110000000011111111222210121012
10012200011122000000122220111222111110001122001112200012220112220000111111111220112011111211112211110001201222001111122220001112110000122012222200111220011112220011000122220011122200111222111112012210
11100101102202001222000222022012111121221202220120200211122021220011000001122020111211122200120200221122200012010122200120220022011222212120122202111110200122221101011200220102201112011001001220212210
10010010100211012022012002101022011102022202010100201022212210220102000000122221000101102222101102110011012201100000222221022221222000112120201220112110100120011220000202001100211220012010110212012102
01222120010102120102112012000102102201000011222210211201120120001202011120101002020122221100200210010102011211211122212011020022200011001012112201121011001120202121211100120002000021001222110212010000
11222121020211021122212221102012121100112002010002120000110202122120200012010001212210121002112201200111202101010101221220101210220201101022011121222210210211100200002101101021202222111221110022101120
21210111001222011012120120020020211201201001211222111120022010212021202202102102021110122220000211002012222110222202102212102120021222201211100211220202100112112100102022202101212212202121122010120111
00000110111000110111200221120010100212002022021022221012112111100021211211102110020210110221120220200022220022012021001200221111201110200201020010010201010211020102022002100120022002001011202110121201
mindist=123
weight enumerator=1 [0]  1952 [123]  2528 [126]  2528 [129]  3120 [132]  3104 [135]  2976
 [138]  1920 [141]  576 [144]  848 [147]  64 [150]  64 [153]  2 [192]  

This is a self-orthogonal code

q=4

q=4 k=6 n=107 d=76

(extension of a code with  automorphisms)
( link )

generator matrix:
[[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[1,1]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[0,0]:[0,0]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[0,0]:
[0,0]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[0,0]:[0,0]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]]
[[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[0,0]:[0,0]:[0,1]:[1,0]:[1,0]:
[1,0]:[1,1]:[1,1]:[0,0]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[0,1]:
[1,0]:[1,0]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:
[0,0]:[0,1]:[1,0]:[1,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[1,1]:[1,1]:
[1,1]:[1,1]:[0,0]:[0,0]:[0,1]:[1,0]:[1,0]:[1,0]:[1,1]:[1,1]:[1,1]:[1,1]:
[1,1]:[0,0]:[0,0]:[0,0]:[0,1]:[0,1]:[0,1]:[0,1]:[1,0]:[1,0]:[1,0]:[1,0]:
[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[0,0]:[0,0]:[0,1]:[0,1]:[0,1]:
[1,0]:[1,0]:[1,0]:[1,0]:[1,1]:[1,1]:[0,0]:[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:
[0,0]:[0,1]:[0,1]:[0,1]:[0,1]:[0,1]:[1,0]:[1,0]:[1,1]:[0,1]:[1,0]]
[[0,0]:[0,0]:[0,1]:[0,1]:[1,0]:[0,0]:[0,0]:[0,1]:[0,1]:[1,1]:[0,1]:[1,0]:
[1,0]:[0,0]:[0,1]:[1,1]:[1,1]:[0,0]:[1,0]:[1,1]:[1,1]:[0,1]:[0,1]:[1,0]:
[0,0]:[1,1]:[0,1]:[1,0]:[1,1]:[1,1]:[1,1]:[0,0]:[1,0]:[1,0]:[0,1]:[1,1]:
[1,1]:[0,0]:[0,0]:[1,1]:[0,0]:[0,1]:[1,0]:[1,1]:[1,1]:[1,1]:[0,0]:[0,1]:
[0,1]:[1,1]:[0,0]:[0,0]:[0,0]:[0,1]:[1,1]:[1,1]:[0,0]:[1,0]:[1,1]:[1,1]:
[1,0]:[0,0]:[0,0]:[0,1]:[0,0]:[0,0]:[1,0]:[1,1]:[0,0]:[0,1]:[0,1]:[1,0]:
[0,1]:[1,1]:[1,1]:[0,0]:[1,1]:[0,0]:[0,0]:[0,0]:[0,1]:[0,0]:[1,0]:[1,1]:
[0,0]:[0,1]:[1,1]:[1,1]:[0,1]:[1,0]:[1,1]:[0,0]:[0,0]:[0,1]:[0,1]:[0,1]:
[1,1]:[0,0]:[0,1]:[0,1]:[1,1]:[1,1]:[0,1]:[1,1]:[0,0]:[1,0]:[0,1]]
[[0,0]:[0,0]:[0,1]:[1,1]:[1,0]:[1,0]:[1,0]:[0,0]:[0,1]:[0,0]:[1,0]:[1,1]:
[1,1]:[0,1]:[0,0]:[0,1]:[1,0]:[0,1]:[0,0]:[0,0]:[0,1]:[1,0]:[1,0]:[1,1]:
[1,1]:[1,0]:[0,1]:[1,1]:[1,0]:[1,1]:[1,0]:[1,0]:[0,1]:[1,0]:[1,0]:[0,1]:
[1,0]:[1,0]:[0,1]:[1,1]:[1,1]:[0,0]:[1,0]:[0,0]:[1,1]:[1,1]:[1,1]:[0,0]:
[1,0]:[1,1]:[0,0]:[1,0]:[0,0]:[1,0]:[0,0]:[1,0]:[1,0]:[0,0]:[0,1]:[1,1]:
[1,1]:[0,0]:[1,1]:[1,0]:[1,1]:[1,1]:[1,0]:[1,1]:[1,1]:[0,1]:[0,1]:[1,1]:
[1,0]:[1,0]:[1,0]:[1,0]:[1,0]:[0,0]:[0,0]:[0,1]:[0,1]:[0,0]:[1,1]:[0,0]:
[0,0]:[0,0]:[1,0]:[1,1]:[1,0]:[0,1]:[1,0]:[0,1]:[1,1]:[0,1]:[0,0]:[1,1]:
[0,0]:[0,1]:[0,1]:[1,0]:[1,0]:[1,1]:[1,0]:[1,1]:[1,0]:[0,1]:[1,1]]
[[0,0]:[0,0]:[1,1]:[0,0]:[0,1]:[0,1]:[0,1]:[1,1]:[0,0]:[1,1]:[1,0]:[0,0]:
[1,1]:[1,0]:[1,1]:[0,0]:[1,0]:[1,0]:[1,1]:[0,1]:[1,0]:[0,0]:[1,1]:[1,0]:
[1,0]:[1,1]:[1,0]:[0,1]:[1,0]:[1,0]:[0,0]:[1,0]:[0,0]:[0,0]:[1,1]:[0,0]:
[1,1]:[0,0]:[0,1]:[0,1]:[0,0]:[1,0]:[1,1]:[0,1]:[1,1]:[0,1]:[0,0]:[0,1]:
[1,1]:[1,1]:[0,1]:[1,1]:[1,1]:[0,0]:[1,0]:[0,0]:[1,0]:[0,1]:[0,0]:[0,0]:
[1,0]:[1,0]:[0,0]:[0,0]:[1,0]:[1,1]:[0,0]:[1,1]:[0,1]:[0,0]:[1,1]:[1,0]:
[0,1]:[0,0]:[0,1]:[0,0]:[0,1]:[0,1]:[1,0]:[1,0]:[0,1]:[0,1]:[1,1]:[1,0]:
[1,0]:[1,0]:[0,1]:[0,1]:[0,0]:[1,1]:[1,1]:[1,0]:[1,1]:[0,0]:[1,1]:[0,0]:
[1,1]:[0,0]:[1,0]:[1,0]:[0,0]:[0,1]:[1,0]:[0,0]:[0,0]:[1,1]:[1,1]]
[[1,1]:[0,0]:[0,0]:[1,1]:[0,0]:[0,1]:[1,1]:[0,0]:[0,1]:[1,0]:[1,1]:[0,0]:
[0,1]:[0,0]:[1,0]:[1,0]:[1,1]:[1,1]:[0,1]:[0,1]:[1,1]:[1,0]:[1,0]:[1,0]:
[1,1]:[0,1]:[1,0]:[0,1]:[1,1]:[0,1]:[0,1]:[1,1]:[0,0]:[0,1]:[0,0]:[0,1]:
[0,1]:[1,1]:[1,1]:[1,0]:[1,1]:[1,0]:[0,1]:[1,0]:[0,0]:[1,1]:[1,1]:[0,0]:
[0,0]:[1,0]:[0,0]:[0,1]:[0,0]:[0,0]:[0,0]:[1,1]:[0,1]:[1,1]:[1,1]:[1,0]:
[1,0]:[1,1]:[0,1]:[1,1]:[1,1]:[0,1]:[0,1]:[1,1]:[0,1]:[1,1]:[0,1]:[0,1]:
[1,0]:[1,0]:[1,0]:[1,0]:[1,0]:[0,1]:[0,1]:[1,1]:[1,1]:[1,1]:[1,0]:[1,1]:
[1,0]:[1,0]:[0,1]:[1,1]:[1,1]:[1,0]:[0,0]:[1,0]:[1,1]:[1,0]:[1,1]:[1,1]:
[1,0]:[1,0]:[1,0]:[1,1]:[0,1]:[0,1]:[0,0]:[0,0]:[0,1]:[0,1]:[0,0]]

mindist=76
weight enumerator=1 [0]  1596 [76]  1170 [80]  885 [84]  345 [88]  99 [92]  

q=4 k=6 n=132 d=96 optimal

(extension of a code with  automorphisms)
( link )


generator matrix:
[[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:
[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
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mindist=96
weight enumerator=1 [0]  2781 [96]  1080 [104]  234 [112]  

q=4 k=6 n=165 d=120

(extension of a code with  automorphisms)
( link )


generator matrix:
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mindist=120
weight enumerator=1 [0]  1920 [120]  1440 [124]  315 [128]  360 [136]  60 [144]  

q=4 k=6 n=193 d=140

(extension of a code with  automorphisms)
( link )


generator matrix:
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mindist=140
weight enumerator=1 [0]  1755 [140]  933 [144]  774 [148]  270 [152]  243 [156]  108 [160
]  12 [172]  

q=4 k=6 n=214 d=156

(extension of a code with  automorphisms)
( link )


generator matrix:
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mindist=156
weight enumerator=1 [0]  2175 [156]  234 [160]  1224 [164]  18 [168]  387 [172]  54 [180
]  3 [208]  

q=4 k=6 n=219 d=160

(extension of a code with  automorphisms)
( link )


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mindist=160
weight enumerator=1 [0]  2409 [160]  1242 [168]  387 [176]  54 [184]  3 [208]  

q=4 k=8 n=91 d=60
(using automorphisms)
( link )

code with group 125961 

generator matrix:
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[[1,0]:[0,0]:[0,1]:[0,1]:[0,0]:[1,1]:[0,0]:[1,1]:[0,1]:[0,0]:[0,0]:[0,0]:
[1,0]:[0,1]:[1,0]:[0,0]:[1,0]:[1,0]:[0,0]:[0,1]:[1,1]:[0,1]:[1,1]:[0,0]:
[0,1]:[0,0]:[0,1]:[0,1]:[1,1]:[1,0]:[1,1]:[1,1]:[1,1]:[0,0]:[0,1]:[1,1]:
[1,0]:[0,1]:[0,0]:[1,0]:[1,0]:[0,1]:[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[0,0]:
[1,0]:[0,0]:[1,0]:[1,0]:[1,0]:[1,0]:[1,0]:[0,0]:[1,1]:[0,1]:[0,0]:[1,0]:
[1,0]:[0,1]:[1,1]:[0,1]:[0,0]:[1,0]:[0,0]:[0,0]:[1,0]:[0,1]:[1,1]:[0,1]:
[1,0]:[0,1]:[1,0]:[1,1]:[1,0]:[1,0]:[0,1]:[0,0]:[0,0]:[0,1]:[0,1]:[0,0]:
[1,1]:[0,0]:[1,0]:[0,0]:[0,1]:[0,0]:[0,1]]

corresponding to the solution:
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mindist=60
weight enumerator=1 [0]  4293 [60]  15060 [64]  23130 [68]  18570 [72]  4257 [76]  225 [80
]  

q=4 k=8 n=97 d=64
(using automorphisms)
( link )

code with group 125961 

generator matrix:
[[0,0]:[0,0]:[0,0]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[0,0]:[0,0]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[0,0]:
[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
[0,0]:[0,0]:[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[0,0]:[0,0]:[1,1]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[0,0]:[0,0]:
[0,0]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
[0,0]]
[[0,0]:[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[0,0]:[0,0]:[0,1]:[0,1]:[0,1]:[1,0]:
[1,0]:[1,1]:[1,1]:[0,0]:[0,0]:[0,0]:[0,0]:[0,1]:[0,1]:[0,1]:[1,0]:[1,0]:
[1,0]:[1,0]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[0,0]:[1,1]:[0,0]:[0,0]:
[0,1]:[0,1]:[0,1]:[0,1]:[0,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
[1,1]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[1,0]:[1,0]:[1,0]:[1,1]:[1,1]:[1,1]:
[1,1]:[1,1]:[0,1]:[1,1]:[1,1]:[0,0]:[0,0]:[1,1]:[1,1]:[0,0]:[0,0]:[0,0]:
[0,1]:[0,1]:[1,0]:[1,0]:[1,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
[1,1]:[1,1]:[0,0]:[0,1]:[0,1]:[0,1]:[0,1]:[1,0]:[1,0]:[1,0]:[1,1]:[0,1]:
[1,1]]
[[0,0]:[0,0]:[0,1]:[1,1]:[0,0]:[0,0]:[1,0]:[1,1]:[0,1]:[1,0]:[1,1]:[0,1]:
[1,1]:[0,1]:[1,0]:[0,1]:[0,1]:[0,1]:[0,1]:[0,0]:[0,1]:[1,0]:[0,1]:[1,0]:
[1,0]:[1,1]:[1,0]:[1,1]:[1,1]:[1,1]:[0,0]:[1,1]:[1,1]:[0,0]:[0,0]:[0,1]:
[0,0]:[0,0]:[1,0]:[1,0]:[1,0]:[0,0]:[0,0]:[0,0]:[1,1]:[0,0]:[0,0]:[0,1]:
[0,1]:[0,0]:[0,0]:[1,0]:[1,0]:[1,1]:[0,0]:[0,1]:[1,1]:[0,0]:[1,0]:[1,1]:
[1,0]:[1,1]:[1,1]:[0,0]:[1,1]:[0,0]:[1,1]:[0,0]:[0,1]:[0,0]:[1,0]:[1,1]:
[0,0]:[0,1]:[0,0]:[0,1]:[0,1]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[0,1]:[1,0]:
[1,0]:[1,1]:[1,1]:[0,0]:[0,1]:[1,1]:[1,1]:[1,0]:[1,1]:[1,1]:[0,0]:[0,0]:
[1,0]]
[[0,0]:[0,0]:[1,0]:[0,1]:[0,0]:[0,1]:[1,0]:[1,0]:[0,1]:[1,0]:[1,1]:[0,0]:
[1,1]:[1,1]:[0,0]:[0,1]:[1,0]:[1,1]:[1,1]:[1,1]:[0,1]:[1,0]:[0,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[1,1]:[0,0]:[1,0]:[1,1]:[0,1]:[0,0]:[0,1]:
[0,1]:[1,1]:[0,0]:[0,0]:[1,0]:[0,0]:[0,1]:[1,1]:[1,0]:[0,0]:[0,1]:[0,1]:
[1,1]:[0,0]:[1,0]:[0,0]:[1,1]:[1,0]:[1,1]:[0,1]:[1,0]:[0,1]:[0,1]:[1,0]:
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[1,0]]
[[0,0]:[0,1]:[0,0]:[0,1]:[0,1]:[1,1]:[0,1]:[0,1]:[0,1]:[0,1]:[1,0]:[0,1]:
[1,1]:[0,1]:[0,0]:[1,0]:[1,0]:[1,0]:[1,1]:[0,0]:[0,1]:[0,1]:[1,0]:[1,1]:
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[0,1]]
[[0,0]:[1,1]:[0,1]:[0,0]:[0,0]:[0,1]:[0,0]:[1,1]:[1,0]:[1,1]:[1,1]:[0,1]:
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[1,0]:[0,0]:[0,1]:[1,0]:[0,1]:[1,1]:[1,1]:[0,1]:[0,0]:[1,0]:[0,0]:[0,1]:
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[0,0]:[0,1]:[1,1]:[0,1]:[1,0]:[1,0]:[1,1]:[0,0]:[1,1]:[0,1]:[0,0]:[1,1]:
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[0,0]:[0,0]:[0,1]:[1,0]:[0,1]:[1,0]:[0,1]:[0,0]:[0,1]:[1,0]:[1,0]:[0,0]:
[1,0]]
[[0,0]:[0,1]:[0,0]:[0,1]:[0,1]:[1,0]:[1,0]:[1,0]:[1,1]:[0,0]:[0,1]:[0,1]:
[0,0]:[0,0]:[0,1]:[0,0]:[1,0]:[0,1]:[0,1]:[1,1]:[0,1]:[1,1]:[1,1]:[0,1]:
[0,0]:[0,1]:[0,1]:[0,1]:[1,1]:[1,0]:[0,0]:[0,1]:[1,0]:[1,1]:[1,0]:[1,1]:
[1,0]:[1,0]:[0,1]:[1,1]:[0,1]:[0,0]:[0,1]:[0,0]:[1,0]:[0,1]:[1,1]:[0,1]:
[0,1]:[0,0]:[1,1]:[1,0]:[1,1]:[0,1]:[0,1]:[0,0]:[1,0]:[1,1]:[1,0]:[0,0]:
[1,0]:[1,0]:[0,1]:[0,0]:[0,0]:[1,0]:[0,0]:[1,0]:[1,1]:[0,0]:[0,1]:[1,1]:
[1,1]:[1,0]:[1,1]:[0,0]:[0,0]:[1,1]:[0,0]:[1,0]:[0,1]:[0,1]:[1,1]:[0,0]:
[0,0]:[0,1]:[0,1]:[1,0]:[1,1]:[0,1]:[0,0]:[0,1]:[0,1]:[0,0]:[0,0]:[0,1]:
[0,1]]
[[1,1]:[1,0]:[0,1]:[0,0]:[1,0]:[0,0]:[1,1]:[1,0]:[1,0]:[0,0]:[1,1]:[1,0]:
[1,1]:[1,1]:[0,0]:[0,1]:[1,0]:[1,0]:[1,1]:[1,0]:[1,0]:[0,1]:[0,0]:[0,0]:
[1,0]:[1,0]:[0,0]:[0,0]:[1,1]:[0,0]:[0,1]:[0,0]:[0,1]:[1,0]:[0,0]:[1,0]:
[0,0]:[1,0]:[1,1]:[0,1]:[1,1]:[1,1]:[0,1]:[1,1]:[0,0]:[0,0]:[1,1]:[1,0]:
[0,0]:[1,0]:[0,0]:[1,1]:[0,0]:[1,1]:[1,0]:[0,1]:[0,0]:[1,1]:[0,0]:[1,0]:
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[1,1]:[0,1]:[1,0]:[1,1]:[0,1]:[0,1]:[0,0]:[0,1]:[0,1]:[0,0]:[0,1]:[0,0]:
[0,1]]

corresponding to the solution:
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mindist=64
weight enumerator=1 [0]  3600 [64]  13725 [68]  22104 [72]  19398 [76]  6300 [80]  405 [84
]  3 [96]  

q=4 k=8 n=113 d=76

(extension of a code with  automorphisms)
( link )

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mindist=76
weight enumerator=1 [0]  5100 [76]  13500 [80]  20160 [84]  18444 [88]  7428 [92]  903 [96
]  

q=4 k=8 n=141 d=96

(extension of a code with  automorphisms)
( link )

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mindist=96
weight enumerator=1 [0]  4614 [96]  11310 [100]  17325 [104]  18645 [108]  10575 [112]  2880
 [116]  138 [120]  45 [124]  3 [136]  

q=4 k=8 n=147 d=100

(extension of a code with  automorphisms)
( link )

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mindist=100
weight enumerator=1 [0]  4125 [100]  9975 [104]  17010 [108]  18792 [112]  11175 [116]  3915
 [120]  495 [124]  45 [128]  3 [140]  

q=4 k=8 n=163 d=112
(using automorphisms)
( link )

code with group 125961 

generator matrix:
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mindist=112
weight enumerator=1 [0]  4539 [112]  10935 [116]  16185 [120]  16695 [124]  11916 [128]  
4725 [132]  495 [136]  45 [140]  

q=4 k=8 n=200 d=138

(extension of a code with  automorphisms)
( link )


generator matrix:
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mindist=138
weight enumerator=1 [0]  1725 [138]  3285 [140]  4500 [142]  5820 [144]  6090 [146]  8010
 [148]  6990 [150]  7485 [152]  6804 [154]  6210 [156]  3915 [158]  2250
 [160]  1665 [162]  555 [164]  135 [166]  48 [168]  48 [170]  

q=4 k=9 n=105 d=68
(using automorphisms)
( link )

code with group 127064 

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[[0,0]:[0,0]:[1,0]:[0,0]:[0,1]:[1,1]:[1,0]:[1,1]:[0,0]:[0,1]:[1,1]:[1,1]:
[1,0]:[1,1]:[1,0]:[0,0]:[1,1]:[1,0]:[1,0]:[1,0]:[1,1]:[0,1]:[1,0]:[0,1]:
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[[0,0]:[1,1]:[1,0]:[1,0]:[1,0]:[1,1]:[1,1]:[1,0]:[0,0]:[1,1]:[0,0]:[1,0]:
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[[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[1,0]:[0,1]:[0,0]:[0,1]:[1,0]:[1,1]:[0,0]:
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[0,1]:[1,1]:[1,1]:[1,0]:[0,0]:[0,1]:[0,1]:[1,0]:[1,0]:[1,1]:[1,1]:[0,0]:
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[1,0]:[0,1]:[0,1]:[1,0]:[1,0]:[1,1]:[0,1]:[1,0]:[0,0]:[1,0]:[0,1]:[1,1]:
[0,0]:[0,1]:[1,1]:[1,0]:[0,0]:[1,0]:[1,0]:[0,0]:[0,0]]

corresponding to the solution:
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mindist=68
weight enumerator=1 [0]  6111 [68]  31437 [72]  72135 [76]  92043 [80]  50085 [84]  9639
 [88]  693 [92]  

q=4 k=9 n=140 d=92
(using automorphisms)
( link )

code with group 127064 

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[0,1]:[0,1]:[0,0]:[1,1]:[0,0]:[1,0]:[1,1]:[0,1]:[1,0]:[1,1]:[0,1]:[0,1]:
[1,1]:[1,0]:[1,0]:[0,1]:[0,1]:[0,1]:[1,1]:[0,1]:[0,1]:[1,1]:[1,0]:[0,0]:
[1,1]:[1,0]:[1,0]:[0,1]:[0,0]:[1,0]:[1,0]:[0,0]:[0,1]:[0,1]:[1,1]:[1,1]:
[1,1]:[0,0]:[1,1]:[1,0]:[0,0]:[0,0]:[0,0]:[0,1]:[1,0]:[1,0]:[1,0]:[0,1]:
[0,0]:[1,1]:[0,1]:[0,1]:[1,1]:[1,1]:[0,0]:[1,0]:[1,0]:[0,0]:[1,1]:[0,0]:
[1,1]:[0,1]:[1,0]:[0,1]:[0,0]:[1,1]:[0,0]:[0,0]]
[[0,0]:[1,1]:[1,1]:[1,0]:[0,1]:[0,0]:[1,1]:[0,0]:[0,0]:[0,1]:[0,1]:[1,0]:
[0,1]:[1,0]:[1,0]:[0,0]:[0,1]:[0,1]:[1,0]:[1,0]:[1,1]:[0,0]:[0,0]:[0,0]:
[1,1]:[1,1]:[0,1]:[0,1]:[0,1]:[1,1]:[1,0]:[1,0]:[1,0]:[1,1]:[1,0]:[0,0]:
[1,1]:[1,0]:[1,1]:[1,0]:[0,0]:[0,1]:[0,1]:[0,1]:[1,0]:[0,0]:[1,0]:[0,1]:
[1,1]:[0,1]:[1,1]:[1,0]:[1,1]:[0,1]:[1,0]:[0,0]:[1,1]:[1,1]:[0,1]:[0,1]:
[1,1]:[0,0]:[0,1]:[0,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[0,1]:[0,0]:[1,1]:
[1,1]:[1,1]:[0,1]:[1,0]:[0,0]:[0,0]:[0,1]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:
[0,0]:[1,0]:[0,1]:[1,1]:[0,1]:[1,0]:[0,1]:[0,0]:[0,0]:[1,1]:[0,1]:[0,1]:
[1,0]:[0,1]:[0,0]:[1,1]:[0,0]:[0,1]:[0,1]:[0,1]:[0,1]:[0,1]:[1,1]:[0,1]:
[1,1]:[1,1]:[1,1]:[0,0]:[0,1]:[1,0]:[1,1]:[0,1]:[0,0]:[1,1]:[0,1]:[1,1]:
[1,0]:[1,0]:[0,0]:[0,1]:[0,1]:[1,1]:[1,1]:[0,0]:[0,1]:[1,0]:[1,1]:[0,1]:
[0,1]:[1,0]:[1,0]:[1,0]:[0,1]:[1,1]:[0,0]:[1,0]]
[[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[1,0]:[0,1]:[0,0]:[0,1]:[1,0]:[1,1]:[0,0]:
[1,0]:[1,1]:[1,0]:[0,0]:[1,0]:[1,0]:[1,0]:[1,1]:[1,1]:[1,1]:[1,1]:[0,1]:
[0,1]:[0,0]:[1,0]:[1,0]:[0,0]:[1,0]:[0,1]:[1,0]:[0,0]:[1,0]:[1,1]:[1,0]:
[1,1]:[1,1]:[1,1]:[0,0]:[0,1]:[0,0]:[0,1]:[1,0]:[1,1]:[0,0]:[1,0]:[0,1]:
[0,1]:[1,0]:[0,0]:[1,1]:[0,0]:[1,1]:[1,0]:[1,1]:[1,1]:[1,0]:[0,1]:[1,1]:
[1,0]:[1,0]:[1,0]:[1,0]:[1,1]:[0,0]:[1,0]:[1,1]:[0,1]:[1,0]:[1,0]:[0,0]:
[1,1]:[0,0]:[1,1]:[1,1]:[1,0]:[0,0]:[1,1]:[1,0]:[1,1]:[0,1]:[1,0]:[0,0]:
[0,1]:[0,1]:[1,1]:[0,0]:[1,0]:[1,0]:[1,0]:[0,0]:[1,0]:[1,0]:[0,1]:[0,0]:
[0,0]:[0,1]:[1,1]:[1,1]:[1,1]:[0,0]:[1,1]:[1,0]:[1,0]:[0,0]:[0,1]:[0,1]:
[1,1]:[1,0]:[1,0]:[0,0]:[1,0]:[0,0]:[1,1]:[1,0]:[1,0]:[1,0]:[0,1]:[0,0]:
[1,1]:[0,1]:[1,1]:[0,0]:[1,1]:[1,0]:[0,1]:[1,1]:[0,1]:[1,1]:[0,0]:[1,0]:
[1,1]:[0,1]:[1,0]:[0,1]:[0,0]:[1,1]:[0,0]:[0,0]]

corresponding to the solution:
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,0,0]
mindist=92
weight enumerator=1 [0]  4221 [92]  18564 [96]  48867 [100]  77301 [104]  70539 [108]  35091
 [112]  6741 [116]  819 [120]  

q=5

q=7

q=7 k=6 n=43 d=31
(using automorphisms)
( link )

code with group 127504 

generator matrix:
0000001111111111111111111111111111111100000
1111113566666444443333311111000000000011111
0001240023466112550022311156113450334423556
0010510040406441231506215645360230353326033
0001330042215151615656653454060104131543043
0124520040316335031116511320162145500464202
corresponding to the solution:
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,0,0,0,0,0,0,0,0]
mindist=31
weight enumerator=1 [0]  1440 [31]  3846 [32]  4536 [33]  8970 [34]  12540 [35]  17250 [36
]  20076 [37]  19518 [38]  15390 [39]  9240 [40]  3840 [41]  906 [42]  
96 [43]  

q=7 k=6 n=60 d=45
(using automorphisms)
( link )

code with group 127569 

generator matrix:
011111111111111111111111001111111111011111111111011111111111
001223444556011113455566110012334456111223334566001133333445
022265015024503341213666065604131653635120043403114601124063
024502440202164453304224343113402626521442640304111342635350
056033033245421411564311214606423110601063020220315542035454
153351530660612346661045344103034236256300122153135613211363
corresponding to the solution:
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mindist=45
weight enumerator=1 [0]  2016 [45]  3816 [46]  3888 [47]  8232 [48]  10152 [49]  13752 [50
]  15312 [51]  17208 [52]  15552 [53]  12288 [54]  8784 [55]  4896 [56
]  1248 [57]  360 [58]  144 [59]  

q=8

q=8 k=5 n=52 d=41
(using automorphisms)
( link )

code with group 59709 

generator matrix:
[[0,0,0]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[0,0,0]:[1,1,1]:
[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:
[1,1,1]:[1,1,1]:[1,1,1]:[0,0,0]:[0,0,0]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:
[1,1,1]:[0,0,0]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[0,0,0]:
[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[0,0,0]:[1,1,1]:
[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]]
[[0,0,0]:[0,0,0]:[0,0,0]:[0,1,0]:[1,0,1]:[1,1,0]:[1,1,1]:[1,1,1]:[0,0,0]:
[0,0,1]:[0,1,0]:[1,0,0]:[1,1,0]:[1,1,1]:[0,0,0]:[0,1,1]:[0,1,1]:[0,1,1]:
[1,1,0]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,0]:[1,1,0]:[1,1,1]:[1,1,1]:
[1,1,1]:[1,1,1]:[0,0,1]:[0,1,0]:[0,1,1]:[1,0,0]:[1,0,1]:[1,1,1]:[1,1,1]:
[0,0,0]:[0,0,1]:[1,0,0]:[1,0,1]:[1,1,1]:[1,1,1]:[1,1,0]:[1,1,1]:[0,1,1]:
[1,0,0]:[1,0,0]:[1,0,0]:[1,0,1]:[1,0,1]:[0,0,0]:[0,0,0]]
[[0,0,0]:[0,1,1]:[1,1,1]:[0,1,0]:[1,1,0]:[1,0,0]:[1,1,1]:[1,1,0]:[0,0,0]:
[0,0,1]:[1,0,1]:[0,1,1]:[0,1,0]:[1,1,1]:[1,1,0]:[0,0,0]:[1,0,0]:[1,1,1]:
[1,0,1]:[0,0,1]:[1,1,1]:[0,0,1]:[1,0,1]:[1,1,0]:[1,1,1]:[0,0,0]:[0,0,1]:
[1,0,1]:[1,1,1]:[0,0,0]:[1,0,1]:[1,0,1]:[1,0,1]:[1,0,0]:[1,0,0]:[0,1,0]:
[1,0,0]:[1,1,1]:[0,1,0]:[1,0,1]:[0,0,0]:[0,1,0]:[0,0,0]:[1,1,1]:[0,0,1]:
[0,0,1]:[0,1,0]:[1,1,0]:[0,0,0]:[1,0,0]:[1,0,1]:[1,0,1]]
[[0,0,0]:[1,0,1]:[1,0,1]:[0,0,0]:[1,1,0]:[0,0,0]:[0,1,0]:[0,1,0]:[1,1,1]:
[1,1,0]:[0,1,1]:[0,0,1]:[1,1,1]:[1,1,0]:[0,1,1]:[1,0,1]:[1,1,1]:[0,1,1]:
[1,0,0]:[1,0,1]:[1,1,1]:[0,1,1]:[1,1,1]:[0,1,1]:[1,0,1]:[1,1,1]:[1,1,1]:
[1,0,1]:[1,0,1]:[0,1,0]:[1,1,0]:[0,1,0]:[1,0,0]:[1,0,0]:[0,0,1]:[0,1,1]:
[1,0,0]:[1,0,1]:[1,1,0]:[0,1,1]:[0,1,0]:[1,0,0]:[1,0,0]:[0,0,0]:[1,0,1]:
[1,1,0]:[0,1,0]:[1,1,0]:[1,0,0]:[1,1,0]:[0,1,0]:[0,0,1]]
[[1,1,1]:[0,1,1]:[1,0,0]:[1,1,1]:[1,1,0]:[1,0,0]:[0,1,1]:[1,1,1]:[1,1,0]:
[0,0,0]:[1,0,1]:[0,1,0]:[1,1,0]:[1,0,0]:[0,0,0]:[0,1,1]:[1,0,1]:[1,0,0]:
[0,0,0]:[0,0,0]:[0,1,0]:[0,0,1]:[0,1,0]:[0,0,0]:[0,1,1]:[0,0,1]:[1,0,1]:
[0,0,1]:[1,1,0]:[0,0,1]:[0,1,0]:[1,0,0]:[1,0,1]:[0,1,0]:[0,0,1]:[1,1,0]:
[1,0,0]:[0,0,0]:[0,1,0]:[0,1,0]:[0,1,1]:[1,0,0]:[0,0,1]:[0,1,1]:[0,1,0]:
[0,0,0]:[1,1,0]:[1,1,1]:[0,0,0]:[0,0,0]:[1,1,1]:[0,0,0]]

corresponding to the solution:
[1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0
,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,1,1]
mindist=41
weight enumerator=1 [0]  1960 [41]  2016 [42]  3381 [43]  4263 [44]  4165 [45]  4165 [46
]  5733 [47]  3920 [48]  2163 [49]  707 [50]  294 [51]  

q=8 k=5 n=73 d=59
(using automorphisms)
( link )

code with group 59709 

generator matrix:
[[0,0,0]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[0,0,0]:[0,0,0]:
[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:
[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:
[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[0,0,0]:
[0,0,0]:[0,0,0]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[0,0,0]:[1,1,1]:[1,1,1]:
[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[0,0,0]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:
[1,1,1]:[1,1,1]:[0,0,0]:[0,0,0]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:
[1,1,1]:[0,0,0]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:
[1,1,1]]
[[0,0,0]:[0,0,0]:[0,0,0]:[0,1,0]:[1,0,1]:[1,1,0]:[1,1,1]:[1,1,1]:[1,1,1]:
[0,0,0]:[0,1,0]:[0,1,0]:[1,0,0]:[1,1,1]:[0,0,0]:[0,0,1]:[0,1,1]:[1,1,0]:
[1,1,0]:[1,1,1]:[1,1,1]:[0,0,0]:[0,0,1]:[0,1,0]:[1,0,1]:[1,0,1]:[1,1,0]:
[1,1,1]:[0,0,1]:[0,0,1]:[0,1,0]:[1,0,0]:[1,0,0]:[1,0,1]:[1,1,1]:[1,1,1]:
[1,1,1]:[1,1,1]:[0,1,0]:[0,1,1]:[1,0,1]:[1,1,0]:[1,1,1]:[0,0,0]:[0,1,0]:
[0,1,0]:[0,1,1]:[1,1,0]:[1,1,0]:[1,1,1]:[0,0,1]:[0,1,0]:[0,1,1]:[1,0,1]:
[1,0,1]:[1,1,0]:[0,0,0]:[1,1,1]:[0,0,0]:[0,0,0]:[0,1,1]:[1,0,0]:[1,1,0]:
[1,1,0]:[1,1,1]:[0,0,1]:[0,1,0]:[0,1,0]:[1,0,0]:[1,0,1]:[1,0,1]:[0,0,1]:
[0,0,0]]
[[0,0,0]:[0,1,1]:[1,1,1]:[0,1,0]:[1,1,0]:[1,0,0]:[1,1,1]:[1,0,1]:[1,1,0]:
[0,0,1]:[0,0,0]:[0,1,0]:[1,1,0]:[1,1,1]:[1,1,1]:[0,1,1]:[1,0,0]:[0,0,0]:
[0,1,0]:[0,1,0]:[1,1,0]:[1,1,0]:[1,1,0]:[1,0,1]:[1,1,0]:[1,1,1]:[0,0,0]:
[1,1,0]:[0,0,0]:[0,1,0]:[0,1,1]:[1,0,0]:[1,1,1]:[0,1,1]:[1,0,1]:[0,0,0]:
[1,0,0]:[1,1,1]:[0,1,1]:[1,0,0]:[1,0,1]:[1,0,1]:[0,1,0]:[1,1,1]:[0,0,0]:
[0,0,1]:[1,1,1]:[0,1,1]:[1,0,0]:[1,0,1]:[0,0,1]:[1,1,1]:[1,1,0]:[0,0,0]:
[1,1,1]:[0,1,0]:[1,1,1]:[0,1,0]:[1,0,1]:[1,1,1]:[0,0,0]:[0,1,1]:[0,0,1]:
[0,0,0]:[1,0,1]:[0,0,1]:[0,0,0]:[1,0,1]:[1,0,0]:[0,1,1]:[1,1,1]:[0,0,0]:
[1,0,1]]
[[0,0,0]:[1,0,1]:[1,0,1]:[0,0,0]:[1,1,0]:[0,0,0]:[0,1,0]:[0,0,0]:[1,1,1]:
[0,0,1]:[0,0,0]:[0,1,1]:[0,1,0]:[0,1,1]:[0,0,1]:[0,0,0]:[0,0,0]:[1,1,0]:
[1,1,0]:[0,0,0]:[1,1,1]:[1,0,0]:[1,1,1]:[1,0,1]:[1,1,1]:[1,0,1]:[0,0,0]:
[1,0,1]:[1,1,1]:[0,1,0]:[0,1,0]:[1,1,1]:[1,0,0]:[0,0,1]:[1,1,1]:[1,0,0]:
[0,0,0]:[0,0,0]:[1,1,0]:[0,0,1]:[1,1,1]:[1,1,0]:[1,0,1]:[0,1,1]:[1,0,1]:
[1,1,1]:[0,1,1]:[1,0,1]:[0,0,1]:[1,0,1]:[1,0,0]:[0,1,1]:[0,0,1]:[0,1,1]:
[1,1,0]:[1,0,0]:[0,0,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,0,1]:[1,1,0]:[0,0,1]:
[1,0,0]:[1,1,0]:[1,0,1]:[0,1,1]:[0,1,1]:[0,0,0]:[1,1,0]:[0,0,1]:[1,1,0]:
[0,0,1]]
[[1,1,1]:[0,1,1]:[1,0,0]:[1,1,1]:[1,1,0]:[1,0,0]:[0,1,1]:[0,1,1]:[1,0,1]:
[0,1,0]:[1,1,0]:[1,1,1]:[1,0,1]:[1,0,0]:[0,0,0]:[1,1,0]:[1,0,0]:[0,1,0]:
[1,0,0]:[1,1,1]:[0,1,1]:[0,1,0]:[0,1,1]:[0,0,1]:[1,1,0]:[1,1,1]:[1,1,1]:
[0,0,1]:[1,1,0]:[0,0,0]:[0,1,1]:[1,0,0]:[0,0,0]:[1,0,1]:[0,0,0]:[1,0,1]:
[1,0,0]:[1,0,1]:[1,0,0]:[1,1,1]:[0,0,0]:[1,0,0]:[0,1,1]:[0,0,1]:[1,1,1]:
[0,1,0]:[0,0,1]:[0,0,0]:[1,1,0]:[0,0,1]:[1,0,1]:[0,0,0]:[1,0,1]:[0,0,0]:
[1,0,0]:[0,0,0]:[0,0,1]:[0,0,1]:[1,1,1]:[1,0,1]:[0,1,0]:[0,1,1]:[1,1,1]:
[0,0,1]:[1,0,0]:[0,0,0]:[1,1,1]:[1,0,0]:[1,1,1]:[1,1,1]:[1,0,0]:[0,0,1]:
[0,0,0]]

corresponding to the solution:
[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
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,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,1,0,0,1]
mindist=59
weight enumerator=1 [0]  1666 [59]  3234 [60]  2548 [61]  3822 [62]  4263 [63]  2646 [64
]  4557 [65]  3479 [66]  2989 [67]  2107 [68]  931 [69]  455 [70]  70 [71
]  

q=8 k=5 n=81 d=66
(extension of a code with automorphisms)
( link )

generator matrix:
[[0,0,0]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[0,0,0]:[0,0,0]:
[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:
[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:
[1,1,1]:[0,0,0]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:
[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[0,0,0]:[0,0,0]:[0,0,0]:
[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:
[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:
[0,0,0]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[0,0,0]:[1,1,1]:
[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]:[1,1,1]
]
[[0,0,0]:[0,0,0]:[0,0,0]:[0,1,0]:[1,0,1]:[1,1,0]:[1,1,1]:[1,1,1]:[1,1,1]:
[0,0,0]:[0,1,0]:[0,1,0]:[1,0,0]:[1,1,1]:[0,0,0]:[0,0,0]:[0,0,0]:[0,1,0]:
[1,0,0]:[1,1,1]:[1,1,1]:[0,1,0]:[0,1,0]:[1,0,0]:[1,0,1]:[1,1,0]:[1,1,0]:
[1,1,1]:[1,1,1]:[0,0,1]:[1,0,1]:[1,1,0]:[1,1,0]:[1,1,1]:[1,1,1]:[0,1,0]:
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[0,0,1]:[0,1,1]:[1,1,1]:[1,1,1]:[0,0,1]:[0,1,0]:[0,1,1]:[0,1,1]:[1,0,1]:
[1,1,0]:[1,1,1]:[0,0,1]:[0,1,0]:[0,1,1]:[1,0,0]:[1,0,1]:[1,1,0]:[1,1,1]:
[1,1,1]:[0,0,1]:[0,1,1]:[0,1,1]:[0,1,1]:[1,0,1]:[1,1,0]:[1,1,1]:[0,0,1]:
[0,1,0]:[0,1,1]:[1,0,1]:[1,0,1]:[1,1,0]:[1,1,0]:[0,1,0]:[0,0,0]:[0,0,1]
]
[[0,0,0]:[0,1,1]:[1,1,1]:[0,1,0]:[1,1,0]:[1,0,0]:[1,1,1]:[1,0,1]:[1,1,0]:
[0,0,1]:[0,0,0]:[0,1,0]:[1,1,0]:[1,1,1]:[0,0,0]:[0,0,1]:[1,0,1]:[1,0,0]:
[0,1,1]:[1,1,0]:[1,1,1]:[0,0,1]:[1,1,1]:[1,1,0]:[1,0,0]:[1,0,1]:[1,0,1]:
[1,0,1]:[1,1,1]:[1,1,0]:[1,0,1]:[0,0,0]:[1,1,0]:[1,0,1]:[1,0,1]:[1,1,1]:
[1,1,0]:[0,0,1]:[1,0,0]:[1,1,0]:[0,0,0]:[1,0,0]:[1,1,1]:[1,0,0]:[1,0,1]:
[0,1,1]:[0,0,0]:[0,1,1]:[1,0,0]:[0,0,1]:[1,1,1]:[0,1,1]:[1,0,0]:[0,0,0]:
[1,1,1]:[0,1,0]:[0,1,0]:[1,0,1]:[0,0,1]:[0,1,0]:[0,1,0]:[0,1,0]:[0,0,0]:
[0,0,0]:[1,0,0]:[1,0,0]:[1,0,1]:[1,1,1]:[1,0,1]:[0,1,0]:[1,0,1]:[0,0,1]:
[1,1,1]:[1,1,0]:[0,0,0]:[1,1,1]:[0,1,0]:[0,0,0]:[0,0,0]:[1,0,1]:[0,0,0]
]
[[0,0,0]:[1,0,1]:[1,0,1]:[0,0,0]:[1,1,0]:[0,0,0]:[0,1,0]:[0,0,0]:[1,1,1]:
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]
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]

mindist=66
weight enumerator=1 [0]  3479 [66]  6027 [68]  7455 [70]  7399 [72]  5733 [74]  2205 [76
]  469 [78]  

q=8 k=5 n=109 d=90
(extension of a code with  automorphisms)
( link )

generator matrix:
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[1,1,1]]
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[0,0,0]]
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[0,1,0]]
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[1,1,1]]

mindist=90
weight enumerator=1 [0]  3283 [90]  6370 [92]  5929 [94]  6272 [96]  5397 [98]  3920 [100
]  1323 [102]  245 [104]  28 [106]  

q=9