The generator matrix

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

generates a code of length 87 over Z2[X]/(X^2) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+95x^82+113x^84+122x^86+60x^88+38x^90+17x^92+22x^94+14x^96+4x^98+10x^100+4x^102+3x^104+2x^106+4x^108+2x^112+1x^114

The gray image is a linear code over GF(2) with n=174, k=9 and d=82.
This code was found by Heurico 1.10 in 0.031 seconds.