The generator matrix

1 0 0 0 0 1 1 1 0 1 1 X 0 1 1 X 0 1 1 X 0 1 0 1 1 0 1 X 1 X 1 X 1 1 X X 1 X 0 1 1 0 X 1 1 1 1 0 0 X 0 X 1 1 0 0 1 0 X X X 1 0 1 1 1 X X 1 1 1 X 0 0 0 1 1 1 1 0 1 1 0 1 1 1 1
0 1 0 0 0 0 0 0 X 0 X X X 0 X 0 X 1 X+1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 X 1 1 X X+1 X 1 0 1 X X 1 0 0 1 0 X+1 X 1 1 0 X 0 X 1 0 0 1 X 0 1 1 1 X X 1 1 1 0 X+1 1 0 X 0 0 0 0 X+1 X+1 X+1 0
0 0 1 0 0 0 0 X 0 1 1 1 1 1 X+1 1 X X 1 X 1 X+1 1 0 0 X X+1 X 0 1 X+1 1 1 X+1 X+1 1 X+1 0 0 0 X 0 X X X X X X+1 1 1 X 1 0 1 1 X+1 X 1 0 1 0 1 1 X X 0 X+1 1 X 1 1 X X 0 1 X+1 0 0 1 X X+1 0 X X X 0 1
0 0 0 1 0 1 0 1 1 1 0 X 1 X+1 0 X+1 X 1 X X+1 X X+1 X+1 1 X 0 X+1 X+1 0 1 X 0 X+1 X+1 1 X+1 0 0 X X+1 1 1 1 X X X+1 X 0 X+1 X 0 0 0 1 1 1 0 0 1 X X 0 X+1 1 X X+1 X+1 1 X X X+1 0 1 0 1 1 X+1 X+1 1 1 0 X 0 X+1 1 X+1 1
0 0 0 0 1 1 X+1 0 1 X X X+1 0 X+1 1 1 1 X+1 1 X X 0 1 0 X 1 X+1 X+1 1 0 0 1 1 X+1 0 X+1 1 0 1 1 X 1 X 0 X+1 X 1 1 X 0 X+1 X+1 X+1 X 1 X X+1 0 X X+1 X+1 0 1 1 0 0 X+1 X+1 X X+1 0 0 0 X+1 X+1 X 1 0 0 X X X+1 1 1 1 0 0
0 0 0 0 0 X X 0 X 0 0 X 0 X X X X X X 0 0 0 X 0 0 X X X X 0 X 0 0 0 X 0 0 X 0 0 X 0 X X 0 X 0 0 X X 0 0 0 X 0 0 0 X X 0 0 X 0 0 X 0 0 X X 0 0 0 X X 0 0 X X X 0 0 X X X X 0 0

generates a code of length 87 over Z2[X]/(X^2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+64x^78+106x^79+106x^80+166x^81+141x^82+124x^83+138x^84+144x^85+122x^86+102x^87+121x^88+94x^89+79x^90+60x^91+69x^92+74x^93+51x^94+42x^95+42x^96+42x^97+34x^98+28x^99+25x^100+20x^101+17x^102+14x^103+10x^104+2x^105+2x^106+4x^107+2x^109+2x^110

The gray image is a linear code over GF(2) with n=174, k=11 and d=78.
This code was found by Heurico 1.10 in 0.296 seconds.