The generator matrix
1 0 0 0 1 1 1 X 0 0 0 1 1 1 1 0 X 1 1 1 0 1 0 X X 1 0 1 1 0 X 1 1 X 1 1 1 X X 1 X 1 0 0 1 0 0 1 1 X 1 1 1 X 1 X 1 X X X 0 X 1 1 1 1 1 1 X X 1 1 X 1 1 X 1 1 1
0 1 0 0 0 0 0 0 1 1 1 1 X+1 1 1 X 1 1 X 1 X 0 0 1 1 X+1 0 X+1 0 1 X 0 X+1 1 X+1 X X+1 1 X 0 X X 1 X 1 0 X 0 X+1 0 X 0 1 X X 1 X 1 1 0 1 1 1 X+1 0 X+1 X 1 1 0 1 X 0 X 0 1 1 X 0
0 0 1 0 0 1 1 1 X 1 X+1 1 1 X 0 0 X 0 X+1 X+1 1 0 1 1 0 1 1 X+1 1 1 1 X X 0 0 0 1 1 X X+1 1 X+1 X+1 1 X+1 0 1 X X+1 0 X 1 X+1 0 X+1 X 1 0 X 1 X+1 X+1 X 1 X+1 X X+1 1 X 1 1 1 1 X 1 X 1 0 0
0 0 0 1 1 1 0 1 1 X+1 X 0 1 X+1 X 1 1 1 X 0 X 0 X+1 X X 1 X X X+1 1 1 X+1 0 X+1 X X X+1 X 1 X 0 X 0 X+1 X 1 1 0 0 1 1 X X+1 1 1 1 X+1 X+1 X+1 1 1 1 X+1 1 1 X 0 X 1 X+1 0 X X 1 0 X+1 X X X
0 0 0 0 X 0 0 0 0 0 0 X X X X X X 0 0 0 X X X 0 X X 0 X X 0 X X X 0 0 X 0 X 0 0 0 0 X X 0 0 0 0 0 X 0 0 X X 0 0 X 0 X 0 0 X X 0 0 0 X X X 0 0 0 X 0 X X X X X
0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X X X X X X X X X X 0 X X X X X 0 X X 0 X 0 0 X X X 0 0 X 0 X 0 0 X X X X X 0 X X 0 X 0 X
0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X 0 X 0 X X X 0 0 X X X X 0 0 0 X X 0 0 X 0 0 0 X X X X X 0 0 0 X X 0 0 X 0 X 0 X X 0 X X X 0 X 0 0 X X
generates a code of length 79 over Z2[X]/(X^2) who´s minimum homogenous weight is 70.
Homogenous weight enumerator: w(x)=1x^0+53x^70+84x^71+113x^72+166x^73+125x^74+134x^75+158x^76+134x^77+140x^78+122x^79+92x^80+100x^81+86x^82+74x^83+73x^84+60x^85+59x^86+56x^87+42x^88+26x^89+32x^90+38x^91+29x^92+22x^93+13x^94+2x^95+4x^96+4x^97+1x^98+2x^99+3x^102
The gray image is a linear code over GF(2) with n=158, k=11 and d=70.
This code was found by Heurico 1.16 in 0.774 seconds.