The generator matrix

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

generates a code of length 86 over Z2[X]/(X^2) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+50x^77+107x^78+130x^79+153x^80+152x^81+136x^82+138x^83+129x^84+114x^85+105x^86+94x^87+84x^88+94x^89+75x^90+68x^91+81x^92+50x^93+48x^94+44x^95+45x^96+40x^97+21x^98+24x^99+16x^100+10x^101+16x^102+12x^103+1x^104+2x^105+4x^106+2x^107+2x^108

The gray image is a linear code over GF(2) with n=172, k=11 and d=77.
This code was found by Heurico 1.10 in 0.297 seconds.