new linear codes from 080808

• binary: 1 optimal + 2 improvements + 3 derived
• ternary: 3 improvements + 4 derived
• q=4: 5 improvements + 7 derived
• q=5: 2 improvements + 2 derived

binary q=2

q=2 k=14 n=51 d=18 optimal
(using automorphisms)
( link )

it is a [51,14,18] code with group 126786 
generator matrix:
000000011111000011111111000000011111000000000111001
000011100111000100011111000000100001000111111011000
011100111001001100100001000111100111000000111000111
001100011011111001000011000011001001111001111111011
010001001111111001101110001001111010111110001101101
010110101011010001001111110010010111011000011111111
001110110111010110101111010101101100001010011011000
101000010110110100100011000001000000110101001101111
011010100011001111110110001010111100111101010011110
110011001110010101001000011100011011000110001101001
000001001110011100110111001010000110100001110101011
010110111000000100011010011010011010110010110111101
010101110000000110010100001000101000100000101011010
111111111111000000000000111111111111111111111111000
corresponding to the solution:
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,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
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,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
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,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0
,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]
mindist=18
weight enumerator=1 [0]  639 [18]  1200 [20]  2079 [22]  3265 [24]  3519 [26]  3105 [28]  
1671 [30]  642 [32]  210 [34]  43 [36]  6 [38]  4 [42]  

q=2 k=15 n=172 d=74 
(using automorphisms)
( link )

there is a [172,15,74] code with group 125985 
generator matrix:
0000000000001111111111111111000000000000111111111111111100000000000011111111111111110000000000001111111111111111000000000000000011111111111100000000000011111111111111110000
0000111111110000000000111111000000111111000000001111111100000011111100000000111111110000001111110000111111111111000000000011111100001111111100000000111100000011111111110011
0111000001110000000011111111000001000111001111110000111100001100001100000111000001110001110001110011000000111111000000111100001100010000011100000111011100111100000011110101
1011011110010000001111000011001110111000010001110000111100110101111100001001001110010110110110110111001111000111000111111101110001100000100100011000000011000100000100000110
0111000000010001110000000111110000000011111111110111011101110100111100110000010010111011000010110111011111000000011111011100010111110011011000111001100100011000011101111100
0101101111100110011101001111111110011100110010111111100001010100110101001111101100001000110101010100100111011001100000011100100111110100111001000011011101001100101110011100
0101110000111000011101110001110111101100100010001011000110111001011100011111100110111110000011010101001011100011011111100010101100011000011000111010101011010001011100101010
1111100011101110001100111101001110000111110000001011011100111010111100011000011100100100111100011100001011100110001011000000110100111101101110101100000001101001101111010101
0011010000101011111101010111110001011001110100001001000110000000111001001001110011101101010000111001000001001101110101101110000001111110010100011100111010101011111100100000
1011110001111010100101111011011111010110101001000010011011010100001110000010111110101011111011111000001100000010000010000001000000010001001111101110100100011010111000001100
0100110010110110101010000111100011111000110000010011101110000101001000100111000001011010000100100110001000011001000010100101110000101010010010011000010011011100110001111100
1001011100010011001111100111011011110011001110010100101110100001110100100100001101010001111011110001110000111101111101111101000000100101101101111110010110100000110110110000
0001010000110111101010001111010010010001100111010110110111111111100101111111010111010000010100110110101101110101110001010001111010000111011011101110010101100111111000111010
1110010111101001101001001110010001001100010001000100100001011100010110010101111111000111001000110010010000100111111101101101001011001010010110100110000000000010010000110000
0100100010101101110100111010010111010111010011111011100110010011001100001101011101011010101011110110111101110010001110001011111110110111011001100011110010101000110011100101
corresponding to the solution:
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0
,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
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,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
mindist=74
weight enumerator=1 [0]  2184 [74]  1225 [76]  1008 [78]  1470 [80]  8568 [82]  1400 [84
]  1056 [86]  1400 [88]  8568 [90]  1470 [92]  1008 [94]  1225 [96]  2184
 [98]  1 [172]  

q=2 k=15 n=175 d=76 
(using automorphisms)
( link )

there is a [175,15,76] code with group 125985 
generator matrix:
0000000000001111111111111111000000000000111111111111111100000000000011111111111111110000000000001111111111111111000000000000000011111111111100000000000011111111111111110000000
0000111111110000000000111111000000111111000000001111111100000011111100000000111111110000001111110000111111111111000000000011111100001111111100000000111100000011111111110100111
0111000001110000000011111111000001000111001111110000111100001100001100000111000001110001110001110011000000111111000000111100001100010000011100000111011100111100000011111101010
1011011110010000001111000011001110111000010001110000111100110101111100001001001110010110110110110111001111000111000111111101110001100000100100011000000011000100000100001001101
0111000000010001110000000111110000000011111111110111011101110100111100110000010010111011000010110111011111000000011111011100010111110011011000111001100100011000011101110111001
0101101111100110011101001111111110011100110010111111100001010100110101001111101100001000110101010100100111011001100000011100100111110100111001000011011101001100101110010111001
0101110000111000011101110001110111101100100010001011000110111001011100011111100110111110000011010101001011100011011111100010101100011000011000111010101011010001011100101110100
1111100011101110001100111101001110000111110000001011011100111010111100011000011100100100111100011100001011100110001011000000110100111101101110101100000001101001101111011101010
0011010000101011111101010111110001011001110100001001000110000000111001001001110011101101010000111001000001001101110101101110000001111110010100011100111010101011111100100000000
1011110001111010100101111011011111010110101001000010011011010100001110000010111110101011111011111000001100000010000010000001000000010001001111101110100100011010111000000111001
0100110010110110101010000111100011111000110000010011101110000101001000100111000001011010000100100110001000011001000010100101110000101010010010011000010011011100110001110111001
1001011100010011001111100111011011110011001110010100101110100001110100100100001101010001111011110001110000111101111101111101000000100101101101111110010110100000110110110000000
0001010000110111101010001111010010010001100111010110110111111111100101111111010111010000010100110110101101110101110001010001111010000111011011101110010101100111111000111110100
1110010111101001101001001110010001001100010001000100100001011100010110010101111111000111001000110010010000100111111101101101001011001010010110100110000000000010010000110000000
0100100010101101110100111010010111010111010011111011100110010011001100001101011101011010101011110110111101110010001110001011111110110111011001100011110010101000110011101101010
corresponding to the solution:
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0
,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
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,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
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0
,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
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0
,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
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0
,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
,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,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
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1]
mindist=76
weight enumerator=1 [0]  3409 [76]  2478 [80]  9968 [84]  2456 [88]  10038 [92]  2233 [96
]  2184 [100]  1 [172]  

ternary q=3

q=3 k=8 n=104 d=63 
(using automorphisms)
( link )


there is a [104,8,63] code with group 954 
generator matrix:
00000000111111111111111100000000111111111111111100000000011111111111111100000111111111111111111101110111
00111111000000011111122200001111000011111122222200001111100001111222222201111000000011111111122201110000
11000222000011200002202201111222011200111200112201110022200120012000001210001001111201112222212210120000
00022012002200100020010200222022122202122222021210120200100002220001220102222020112210010111120012011021
12122200112222012202202201000102112121112100111100201001222021200222221120220210012120100001110121022012
02202120011201200210210202001201111210212200012210211022101101210021120010122220200112210001112001110000
11021210021211002102211211010021011112020111212220000111120021211022010120111221120021120012210111200000
21102001102000201022200221101111202212210101112221122201001020112211122201011101202220101000120202220222
corresponding to the solution:
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0
,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
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,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
,0,0,0,0,0,1,0,1,1,0]
mindist=63
weight enumerator=1 [0]  1312 [63]  1536 [66]  576 [69]  1744 [72]  1200 [75]  192 [81]  

q=3 k=9 n=197 d=120
(using automorphisms)
( link )


there is a [197,9,120] code with group 58821 
generator matrix:
00011111111111110000011111111111000000111111111100111111111111110000001111111111000000000111111100000111111111110000000011111111000001111111111100000000111111110000011111111111000000111111111100110
11100000001122220000100001112222001111000111122201000000011111121111110111112222011111111000122200111000111112220000111101112222011110000011112200001111000011120111100000002222000111000011222201021
00111222220001120111000011120012110012022001102211001112200111220011221011220012100000222012200211112012111221120011112200121112101120112200120211111112000101211012212222220001011001001212000111202
11001122220011211012100100021101010120112002200111220120101022111212010012010020201112022012000002111220002020101102110202200020210211120000110002220221011220121122200001220010111121010121022000000
01201000121211020100100002210122222201221011102112011122102201000221102200200122220121012222202111112110020111000220120120010010020022020102201010221001102122020201200120121111212002211222201100220
02222002000100121120200020112020210101121011212221220012102221022220011202222200000100202110102200002110002121121022020012200102120111101211001000010022000012201112201010000102121112221122200122021
00210202112021020020100010001002221202012220010022122212221021010200212101010222002010021211012120222110221100020000020101002100010110010112121112210212001110100120210021111012221010022200102200220
20102001120020202022101001102120001202210121111021221012122200112210010020010022202200210001200122110121100112112012000021100010000020111010220002112222120020002122211210210102111101110120011012110
22101100020001011221121022202100001111111210212111202122022202010000010110112102211100022221022002011211011110220212112000202002020010021211200000021010220021110100112020100111021222012000212110211
corresponding to the solution:
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,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
,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0
,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
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0
,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
,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0
,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
,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1]
mindist=120
weight enumerator=1 [0]  992 [120]  2248 [123]  3312 [126]  2400 [129]  3224 [132]  3360
 [135]  1876 [138]  1264 [141]  648 [144]  288 [147]  32 [150]  32 [153
]  4 [156]  2 [165]  

q=3 k=9 n=211 d=129
(using automorphisms)
( link )


there is a [211,9,129] code with group 58821 
generator matrix:
0001111111111111000111111111111100000111111111110000011111111111000000111111111100000111111111110111111111111111000000111111111100000011111111110000011111111111000111111111111100011111111111110000001111111111110
0010000011122222111011111111222211111000001222220011100011111222001111001111112200011000001222221000111111222222000111000011222200111100011112220111100000122222011000011111222201100000001122220001110011122222021
0100112212200122012000111122012202222122222000120101200211222112010112020011121201100011122000221122000112111222011002012212012211012212200112221000211111001122011011200001000210001111221211120110120201200122112
0011222211202102002201001200121200122200110002121221102212002012111020000202201211111001221022020202001120011011011022211210220111201211201020112001200022101201101100011120002120210012121212200121121000212000000
1221121101012202212101120100100111002112112010102120120100022000221202220121222011201020102200002220000012002222102200111022022012220022001000001022101200002200200012201201122000210220220110121012100021200222220
1212010201200221000111221102021210011001010201122212110010110211221021222012000100110112000001000001012021221201001012222000200210202200210111012001001001200121221112012002222120222022100001122122011021210000111
0211202001110102121002220102110021001201010221222212122202201212101120200021202200120012112122011101121200122110002012010211220211122011000002220211022001112202000021112210121002012120201210202000121022201012220
0112122001111020101012120020111222201202201002022101102101100102100212022110120110211220011221120022121111122200211122211220221002001002200110220200211212221221220022122021200201110210220111020220121020220000020
2001212110011011021221020000101020222120202000021010200222002220011101120222120012210101121101010220011001100001121022212101222222122212020122020120022001110020021111122121001222001012112122112212210010221222121
corresponding to the solution:
[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
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0
,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
,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,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
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0
,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0
,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
,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
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1]
mindist=129
weight enumerator=1 [0]  1158 [129]  1920 [132]  2768 [135]  3368 [138]  2752 [141]  2976
 [144]  1888 [147]  1488 [150]  992 [153]  264 [156]  104 [159]  4 [162
]  

q=4

q=4 k=7 n=109 d=74 
(using automorphisms and extension)
( link )


n=109 q=4 k=7 d=74
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]:[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]:[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]:
[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]:[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]:[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]:[0,0]:[0,1]:[0,1]:[0,1]:[0,1]:[1,0]:[1,0]:[1,0]:
[1,0]:[1,0]:[1,1]:[1,1]:[0,0]:[1,1]:[1,1]:[0,1]:[0,1]:[0,1]:[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]:[1,1]:
[0,0]:[0,0]:[0,0]:[1,0]:[1,0]:[1,0]:[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]:[0,1]:[0,1]:[0,1]:[1,0]:[1,0]:
[1,1]:[1,1]:[1,1]:[0,0]:[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]:[0,0]:[0,0]:[1,1]:[1,1]:[1,1]:[0,0]:
[0,1]:[0,1]:[1,0]:[1,0]:[1,0]:[1,0]:[1,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
[0,0]:[0,0]:[0,0]:[0,1]:[0,1]:[0,1]:[0,1]:[1,0]:[1,0]:[1,0]:[1,1]:[1,1]:
[0,1]]
[[0,0]:[0,0]:[0,1]:[1,1]:[0,0]:[0,0]:[0,0]:[1,0]:[1,1]:[0,0]:[0,1]:[0,1]:
[1,0]:[1,1]:[1,0]:[1,1]:[1,1]:[0,0]:[0,0]:[0,0]:[0,1]:[1,0]:[1,0]:[1,0]:
[1,0]:[1,1]:[0,0]:[0,0]:[1,0]:[1,0]:[1,1]:[1,1]:[1,1]:[1,0]:[1,0]:[1,1]:
[0,1]:[0,1]:[1,1]:[0,0]:[0,0]:[0,1]:[0,0]:[0,1]:[0,1]:[0,1]:[0,1]:[1,1]:
[1,1]:[0,1]:[0,1]:[1,1]:[1,1]:[0,0]:[1,0]:[0,1]:[1,0]:[1,1]:[0,0]:[1,0]:
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[1,1]:[0,0]:[0,1]:[1,0]:[1,0]:[1,1]:[1,1]:[1,1]:[0,0]:[1,0]:[1,1]:[1,0]:
[0,0]:[1,0]:[0,0]:[0,1]:[0,1]:[1,0]:[1,1]:[0,1]:[0,1]:[0,0]:[1,0]:[1,1]:
[0,0]:[0,0]:[1,1]:[0,0]:[0,0]:[0,1]:[1,0]:[0,0]:[1,0]:[1,0]:[0,0]:[0,1]:
[1,0]]
[[0,0]:[0,0]:[0,0]:[1,0]:[0,0]:[0,0]:[0,0]:[1,0]:[1,0]:[1,0]:[0,0]:[0,0]:
[0,0]:[0,1]:[1,0]:[1,1]:[1,0]:[1,0]:[1,0]:[0,1]:[0,1]:[0,0]:[0,0]:[1,0]:
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[1,0]:[1,0]:[0,0]:[0,1]:[1,1]:[0,1]:[0,1]:[1,1]:[0,0]:[0,1]:[0,1]:[1,1]:
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[0,1]:[1,0]:[0,1]:[1,0]:[1,1]:[1,1]:[1,0]:[0,1]:[1,1]:[0,1]:[0,0]:[0,1]:
[0,0]:[0,0]:[0,0]:[0,1]:[0,1]:[0,1]:[1,1]:[0,1]:[1,1]:[1,1]:[1,1]:[1,0]:
[0,0]]
[[0,0]:[1,0]:[0,0]:[0,1]:[1,0]:[1,1]:[1,1]:[0,1]:[0,1]:[1,0]:[0,1]:[1,1]:
[0,0]:[0,0]:[0,1]:[0,1]:[0,0]:[0,0]:[1,1]:[0,0]:[0,1]:[1,0]:[1,1]:[0,1]:
[0,1]:[1,0]:[1,0]:[1,1]:[0,1]:[1,0]:[1,0]:[0,1]:[0,1]:[0,0]:[1,1]:[1,0]:
[0,1]:[0,1]:[0,1]:[1,1]:[0,1]:[0,0]:[1,1]:[0,0]:[1,1]:[0,1]:[1,0]:[1,0]:
[0,1]:[0,1]:[1,0]:[0,1]:[0,1]:[1,0]:[0,0]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:
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[0,1]:[1,0]:[0,1]:[0,1]:[1,0]:[0,0]:[1,0]:[1,1]:[0,1]:[1,0]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[0,0]:[0,0]:[1,0]:[0,0]:[1,0]:[0,0]:[0,1]:
[0,1]:[0,1]:[0,0]:[1,0]:[1,1]:[0,1]:[1,0]:[0,0]:[0,1]:[1,1]:[0,1]:[1,1]:
[1,1]]
[[0,0]:[1,0]:[0,0]:[0,1]:[1,0]:[0,0]:[1,0]:[1,0]:[0,0]:[1,1]:[1,1]:[1,1]:
[1,1]:[1,0]:[1,0]:[1,0]:[0,0]:[0,0]:[1,0]:[1,0]:[1,0]:[0,0]:[1,0]:[0,1]:
[0,1]:[1,0]:[1,1]:[1,0]:[1,1]:[0,1]:[1,1]:[0,0]:[0,0]:[0,1]:[0,1]:[1,0]:
[1,1]:[0,0]:[1,0]:[1,0]:[1,1]:[0,0]:[1,0]:[1,1]:[0,1]:[1,0]:[0,0]:[1,0]:
[0,1]:[0,0]:[0,0]:[1,0]:[1,1]:[0,0]:[0,0]:[1,1]:[0,0]:[0,0]:[0,1]:[0,1]:
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[1,0]:[0,0]:[0,1]:[1,1]:[0,1]:[0,0]:[1,1]:[1,0]:[0,0]:[0,1]:[0,1]:[1,1]:
[0,1]:[1,1]:[0,1]:[1,0]:[1,0]:[0,0]:[0,1]:[0,0]:[0,1]:[1,1]:[0,0]:[1,0]:
[0,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[0,1]:[0,1]:[1,1]:[0,1]:[1,1]:[0,0]:
[0,0]]
[[1,1]:[1,0]:[0,1]:[1,1]:[0,1]:[1,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,0]:[0,1]:
[1,1]:[1,0]:[1,1]:[0,1]:[0,1]:[1,1]:[1,1]:[1,1]:[0,1]:[0,1]:[1,1]:[1,1]:
[0,1]:[1,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,0]:[0,1]:[0,0]:[1,1]:[0,1]:[0,1]:
[0,1]:[1,0]:[1,0]:[0,1]:[1,1]:[0,1]:[1,1]:[1,0]:[1,0]:[1,0]:[1,0]:[1,1]:
[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]:[1,1]:[0,1]:[1,1]:[1,0]:[0,1]:[0,1]:[1,1]:[0,1]:[1,1]:
[0,1]:[0,1]:[1,0]:[1,0]:[0,1]:[0,1]:[0,1]:[1,0]:[0,1]:[1,1]:[1,1]:[1,1]:
[1,0]:[1,1]:[1,0]:[1,0]:[0,1]:[1,1]:[1,0]:[1,0]:[1,1]:[1,1]:[1,1]:[0,1]:
[1,1]:[0,1]:[1,1]:[1,0]:[0,1]:[0,1]:[0,1]:[0,1]:[0,1]:[1,0]:[1,0]:[1,1]:
[0,0]]

mindist=74
weight enumerator=1 [0]  765 [74]  2370 [76]  1788 [78]  2610 [80]  2040 [82]  2613 [84]  
1980 [86]  1305 [88]  720 [90]  189 [92]  3 [106]  

q=4 k=7 n=114 d=78 
(using automorphisms)
( link )

there is a [114,7,78] code with group 36368 
generator matrix:

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

corresponding to the solution:
[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
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,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
,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0
,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
,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,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
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,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
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1]
mindist=78
weight enumerator=1 [0]  1473 [78]  1260 [80]  2655 [82]  2274 [84]  3060 [86]  1512 [88
]  2118 [90]  1035 [92]  675 [94]  315 [96]  3 [108]  3 [114]  

q=4 k=8 n=203 d=140 
(using automorphisms and extension)
( link )

n=203 q=4 k=8 d=140
generator matrix:

[[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:
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mindist=140
weight enumerator=1 [0]  3930 [140]  6135 [144]  12624 [148]  17640 [152]  14145 [156]  7530
 [160]  2715 [164]  630 [168]  183 [172]  3 [196]  

q=4 k=8 n=214 d=148 
(extension using program of J. Zwanzger)
( link )

This is a n=214 k=8 d=148 q=4 code  computed by a program of Johannes Zwanzger
generator matrix:

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mindist=148
weight enumerator=1 [0]  3555 [148]  1530 [150]  3159 [152]  1206 [154]  12498 [156]  5184
 [158]  8118 [160]  2862 [162]  13743 [164]  5562 [166]  2832 [168]  918
 [170]  2700 [172]  1080 [174]  351 [176]  54 [178]  144 [180]  36 [182
]  3 [184]  

q=4 k=8 n=231 d=160
(extension using program of J. Zwanzger)
( link )

This is a n=231 k=8 d=160 q=4 code  computed by a program of Johannes Zwanzger
generator matrix:

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[1,0]:[0,1]:[3]:[0,1]:[0,1]:[0,0]:[1,0]:[3]:[1,0]:[3]:[0,0]:[3]:[0,1]:[0,1]:
[1,0]:[3]:[3]:[3]:[1,0]:[3]:[0,1]:[0,1]:[0,1]:[3]:[0,0]:[3]:[1,0]:[0,0]:
[3]:[1,0]:[0,0]:[0,1]:[0,0]:[3]:[1,0]:[0,0]:[1,0]:[3]:[0,1]:[1,0]:[1,0]:
[3]:[1,0]:[0,0]:[0,0]:[0,0]:[3]:[0,0]:[3]:[3]:[0,0]:[3]:[1,0]:[0,1]:[0,1]:
[1,0]:[1,0]:[0,1]:[1,0]:[0,0]:[3]:[3]:[3]:[1,0]:[3]:[0,0]:[3]:[0,0]:[1,0]:
[0,0]:[0,0]:[3]:[1,0]:[3]:[0,0]:[3]:[3]:[3]:[0,0]:[0,0]:[3]:[0,0]:[3]:[1,0]:
[0,0]:[0,1]:[3]]

mindist=160
weight enumerator=1 [0]  2793 [160]  1062 [162]  4851 [164]  1764 [166]  7881 [168]  3384
 [170]  11184 [172]  4176 [174]  11520 [176]  4500 [178]  5247 [180]  2016
 [182]  2889 [184]  1188 [186]  558 [188]  252 [190]  180 [192]  90 [194
]  

q=5

q=5 k=6 n=79 d=60 
(using automorphisms)
( link )

there is a [82,6,60] code with group 125445 
generator matrix:
0011111111111111111111111111111111111111111111111111111111111111111111111111111111
0011112222333344441111222233334444111122223333444411112222333344441111222233334444
0100000000000000001144223322331144114422332233114422331144114422332233114411442233
0012341234123412341423231414232314231414232314142314231423231423142314231414231423
1021434231132434121432142332412341234132411423143241233241142332140000000000000000
0012343142241343214132412332142314412314233241321441322341143223142314143223414132
corresponding to the solution:
[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
,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
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,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]
mindist=60
weight enumerator=1 [0]  3136 [60]  7496 [65]  4976 [70]  16 [80]  

q=5 k=5 n=81 d=61
(extension using program of J. Zwanzger)
( link )

This is a n=81 k=5 d=61 q=5 code  computed by a program of Johannes Zwanzger
generator matrix:
001111111100011111110001111111001111111100111111110011111111001111111100111111111
112223344411111133441111113344111233334411123333441111114444111233334411000221114
141241403301101304040240141234241013340402440024231311440022032301140122013220014
002003340400110100440100110044444421213344441221333333332222444411223333000113322
202300401440444310243122104020113200044022401332101013240434330343112124132241403
mindist=61
weight enumerator=1 [0]  244 [61]  608 [62]  868 [63]  164 [64]  60 [65]  144 [66]  436 [67
]  304 [68]  72 [69]  4 [70]  12 [71]  64 [72]  76 [73]  24 [74]  12 [77
]  32 [78]