The generator matrix
1 0 0 1 1 1 0 1 1 1 1 0 X 1 0 1 0 1 X 1 X 1 X 1 1 1 0 1 0 1 X 0 1 1 1 1 X 1 0 1 0 1 1 1 1 X 1 1 0 0 X 1 1 X 0 0 0 1 0 1 0 0 0 X X X 1 1 X 1 1 0 0 1 1 1 X X X X 1 1
0 1 0 1 0 1 1 0 0 1 X+1 1 1 X 0 X 0 X+1 1 X+1 1 X+1 1 X X 1 1 1 0 1 0 1 1 X+1 0 X+1 1 X 1 1 1 X 0 X+1 X 0 X+1 X 1 1 1 0 0 X 1 1 1 X+1 1 1 X X 0 1 1 0 X X 1 X 0 0 1 X+1 X+1 X+1 1 1 0 0 X 0
0 0 1 1 1 0 1 0 1 X+1 X X 1 0 1 1 1 X+1 X X 1 X X+1 X X+1 X 0 1 1 X 1 X+1 X 0 1 1 0 X 0 X+1 X+1 X X X X+1 1 X+1 1 X+1 X+1 X X 1 1 X+1 1 1 0 X+1 X+1 1 1 1 0 1 1 1 0 X+1 X 0 1 X+1 X 0 X 1 X 1 1 1 0
0 0 0 X 0 0 0 0 0 X 0 0 0 0 0 0 0 X 0 0 X X X 0 X X X X X X 0 0 X 0 X X 0 X 0 0 0 X 0 X 0 X 0 X X 0 0 0 0 0 X 0 0 X 0 X 0 X X 0 X X 0 X X 0 0 0 X X 0 0 X X X X X 0
0 0 0 0 X 0 0 0 0 0 0 X X X X 0 0 X 0 0 0 0 X X X 0 X 0 X X 0 0 0 X X X X 0 0 0 0 X 0 0 X X X X 0 0 X X 0 0 X 0 X 0 X X X 0 0 0 X 0 0 X 0 X 0 X 0 X 0 X 0 X 0 0 X 0
0 0 0 0 0 X 0 0 0 0 X 0 0 0 0 0 0 0 0 X 0 X 0 0 0 X 0 0 0 X 0 0 X X 0 0 0 0 X X X X X X X X X X X 0 X 0 X X X X 0 X X X X X X 0 X 0 0 0 0 X 0 0 X 0 0 0 X 0 X 0 0 0
0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 0 X X X X X X 0 X 0 0 X X 0 X X X 0 X X 0 0 X 0 X 0 0 0 X X X 0 X 0 0 0 X 0 X 0 X 0 X X X 0 X X 0 0 X X X 0 X X 0 0 X X 0 X 0 X X X X
0 0 0 0 0 0 0 X 0 X X 0 0 0 X X X X 0 X 0 X X 0 X X 0 X 0 0 0 X 0 0 0 0 0 X X 0 X 0 0 X X 0 0 0 X X 0 X X 0 0 0 X 0 X X 0 X X 0 X X X 0 0 0 X 0 0 X 0 0 X X 0 X X X
0 0 0 0 0 0 0 0 X 0 0 X X X X X 0 X 0 0 0 0 X X 0 0 X X 0 X X X X 0 X 0 0 X X 0 0 0 X X 0 X 0 0 0 X 0 X X 0 0 0 0 X 0 0 0 X 0 X X 0 0 X X X X X 0 X 0 0 0 X 0 X X 0
generates a code of length 82 over Z2[X]/(X^2) who´s minimum homogenous weight is 70.
Homogenous weight enumerator: w(x)=1x^0+31x^70+42x^71+117x^72+112x^73+166x^74+210x^75+221x^76+224x^77+223x^78+230x^79+191x^80+250x^81+243x^82+252x^83+192x^84+204x^85+174x^86+170x^87+171x^88+160x^89+115x^90+78x^91+81x^92+52x^93+56x^94+38x^95+40x^96+22x^97+10x^98+4x^99+10x^100+3x^102+1x^106+1x^110+1x^114
The gray image is a linear code over GF(2) with n=164, k=12 and d=70.
This code was found by Heurico 1.16 in 3.5 seconds.