The generator matrix
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 X X X X X X X X 1 1 1 X X X X X 1 1 1
0 X 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X X X X X X X X 0 X 0 X X X X 0 X 0 X 0 0 0 X X 0 X X 0 X X X X X 0 X X 0 X X X X X 0 0
0 0 X 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 X X X X X X X 0 X 0 X 0 0 0 X X X 0 0 0 X 0 0 0 X 0 0 X X 0 0 X X 0 0 X 0 X X 0 X X X X X X 0 0 0
0 0 0 X 0 0 0 0 0 0 0 0 0 X 0 0 0 X X X X X X 0 0 0 X X 0 X X 0 0 0 X 0 0 0 X 0 X X 0 0 X 0 0 X X 0 X 0 X X 0 X 0 X X X X X X X X X X 0
0 0 0 0 X 0 0 0 0 0 0 0 0 X 0 X X X X X X 0 X X 0 X X 0 0 0 0 X X X X 0 0 0 X X 0 0 0 0 0 0 X X X X 0 X 0 0 X X 0 0 0 0 X 0 X 0 0 X X X
0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 X X 0 X X 0 X 0 X 0 X X 0 X X 0 0 0 0 0 0 X X 0 0 0 0 X 0 X X X 0 X X X X 0 0 X 0 0 0 X 0 0 X 0 X X X 0 0
0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 0 X X X X 0 X X 0 X 0 X 0 0 0 0 X X 0 0 X X 0 0 X X 0 0 X X X X X X 0 0 0 X 0 0 0 0 X 0 0 X X X X 0 X X 0
0 0 0 0 0 0 0 X 0 0 0 X 0 0 0 0 X X 0 X 0 0 0 X X X X X X 0 X 0 X X X 0 0 X 0 X X 0 X 0 X X X 0 0 0 X 0 0 0 0 X 0 0 X X 0 0 X 0 0 X X 0
0 0 0 0 0 0 0 0 X 0 0 X 0 0 0 X 0 0 X 0 X 0 0 X 0 0 X 0 X X X 0 X X X 0 X X X 0 X X 0 X 0 X 0 X X X X 0 0 X 0 X X 0 0 X 0 0 0 X 0 0 0 0
0 0 0 0 0 0 0 0 0 X 0 X X X X X 0 0 0 X 0 0 X X 0 0 X 0 X 0 0 X X 0 X X X X 0 0 X X X 0 X X 0 X X 0 X 0 X X X X X X X 0 0 X 0 0 X X 0 0
0 0 0 0 0 0 0 0 0 0 X X X X X 0 0 X X X X X 0 X 0 X 0 X 0 0 0 X 0 0 0 0 0 X 0 X X 0 X X 0 X 0 X X X 0 X X X X 0 0 X 0 0 X 0 X X X X 0 X
generates a code of length 68 over Z2[X]/(X^2) who´s minimum homogenous weight is 54.
Homogenous weight enumerator: w(x)=1x^0+52x^54+124x^56+6x^57+139x^58+16x^59+163x^60+64x^61+173x^62+192x^63+170x^64+326x^65+165x^66+416x^67+131x^68+432x^69+160x^70+320x^71+163x^72+178x^73+153x^74+80x^75+145x^76+16x^77+109x^78+81x^80+2x^81+51x^82+41x^84+16x^86+5x^88+4x^90+1x^94+1x^110
The gray image is a linear code over GF(2) with n=136, k=12 and d=54.
This code was found by Heurico 1.16 in 4.41 seconds.