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 1 0 X X 1 1 1 1 0 1 0 1 1 X 0 X 1 X X 0 0 1 1 1 1 X 1 1 0 X 1 0 1 1 0
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 0 X+1 1 X 0 X+1 1 X+1 X X+1 1 X 0 X X 1 X 1 0 X X+1 0 1 X X 0 X X 0 1 1 1 0 1 1 X 1 0 X+1 1 X+1 0 1 X X X X 0 X+1 X+1 X
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 1 X+1 1 1 X X 0 0 0 1 1 X X+1 1 X+1 X 1 X+1 1 0 1 1 1 X+1 1 1 1 0 X 0 X 1 X X+1 X 1 X+1 0 X 1 0 1 1 1 0 1 0 1 X X 1
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+1 X 1 1 X+1 0 X+1 X X X+1 X 1 X 0 X X X+1 X+1 1 1 X X+1 0 0 X+1 X+1 1 0 0 0 0 0 X X 0 X+1 X+1 X 1 0 0 X X X+1 1 0 X+1 1 X X 0
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 0 X X 0 X 0 0 0 X X 0 0 0 0 X 0 X X 0 X X 0 X X 0 0 X X 0 X 0 X 0 0 X 0
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 X 0 X X X X X X X X X X X X X X 0 X X 0 0 X X X X 0 X X X X X 0 0 X 0 X 0 X X X 0 X X 0 0 0 0 0 0 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 0 X X 0 X X X 0 0 X X X X 0 0 0 0 X X X X 0 X 0 X X 0 0 X 0 X X X X 0 0 X X 0 0 X X X 0 X X X 0 0 X X
generates a code of length 78 over Z2[X]/(X^2) who´s minimum homogenous weight is 69.
Homogenous weight enumerator: w(x)=1x^0+52x^69+97x^70+124x^71+127x^72+136x^73+153x^74+140x^75+132x^76+122x^77+119x^78+110x^79+93x^80+90x^81+100x^82+60x^83+51x^84+72x^85+66x^86+44x^87+23x^88+28x^89+35x^90+24x^91+16x^92+10x^93+5x^94+10x^95+4x^96+2x^97+1x^100+1x^102
The gray image is a linear code over GF(2) with n=156, k=11 and d=69.
This code was found by Heurico 1.16 in 0.787 seconds.