The generator matrix

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

generates a code of length 86 over Z2[X]/(X^2) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+213x^76+386x^78+467x^80+488x^82+454x^84+402x^86+355x^88+348x^90+309x^92+262x^94+197x^96+106x^98+67x^100+18x^102+12x^104+6x^106+5x^108

The gray image is a linear code over GF(2) with n=172, k=12 and d=76.
This code was found by Heurico 1.10 in 7.17 seconds.