The generator matrix

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

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+95x^78+269x^80+301x^82+270x^84+229x^86+192x^88+147x^90+176x^92+112x^94+80x^96+68x^98+52x^100+28x^102+14x^104+12x^106+2x^108

The gray image is a linear code over GF(2) with n=174, k=11 and d=78.
This code was found by Heurico 1.16 in 0.888 seconds.