The generator matrix
1 0 0 1 1 1 0 1 1 1 1 0 X 0 1 1 1 1 X 0 X X 0 1 X 1 1 0 1 1 1 X X 0 1 1 1 0 1 1 1 0 X X X 1 1 0 0 X X X 1 1 1 0 1 1 0 X 1 0 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 1 0 1 1 1 1 0 X 0 1
0 1 0 0 1 1 1 0 0 1 X+1 1 1 0 X X+1 X X+1 1 0 1 0 1 X 1 X+1 X 1 1 X+1 0 1 1 1 0 X X X 1 1 X 0 1 1 1 X+1 0 X 0 X 1 1 X X 1 0 X X+1 1 X 1 1 X 1 0 X+1 1 0 X+1 X X X+1 0 0 1 X 1 X 1 X+1 1 0 0 0 1 1 X
0 0 1 1 1 0 1 0 1 X+1 0 X X+1 1 1 X+1 0 X X 1 X+1 1 0 0 1 X X+1 X+1 1 1 X X 0 0 0 X+1 1 1 0 0 0 1 X+1 X 1 X+1 X 1 1 1 X 1 X+1 X+1 X 1 X X X 1 0 X+1 0 1 X 0 X+1 0 X 1 X+1 0 1 0 X+1 X X X+1 1 X+1 0 1 X 1 1 X+1 1
0 0 0 X 0 0 0 0 0 X X 0 0 0 0 0 0 0 X X X 0 0 X X X X X 0 X 0 X 0 0 X X X 0 X 0 0 X X X 0 X X 0 0 0 0 X X X 0 0 0 X X 0 0 X X X 0 X X 0 0 0 X X 0 0 0 0 0 X X 0 X X X 0 X 0 0
0 0 0 0 X 0 0 0 0 X 0 0 0 X 0 0 X X X X X X 0 X 0 0 X 0 0 0 0 X 0 0 0 0 0 X X X X X 0 0 0 0 X 0 X X X X X X X 0 0 0 X X X 0 X 0 0 0 X X X 0 0 0 X 0 0 0 X 0 X X X X X 0 X X X
0 0 0 0 0 X 0 0 0 0 X 0 0 X 0 X X 0 X X X X 0 X 0 X X 0 0 0 X 0 X X X X 0 0 0 0 X X 0 X X 0 0 X 0 X 0 0 0 X X 0 X 0 0 0 X X 0 X X 0 X 0 0 X X X 0 X 0 X X X 0 X X X 0 0 X X X
0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 0 0 0 0 0 X 0 0 0 X 0 0 X X X X X X X X 0 X X X X X X 0 X X 0 0 X 0 X X X X X 0 X 0 0 0 X 0 X 0 0 0 X 0 0 0 0 X X 0 X X 0 X X 0 X X 0 X 0 0 X 0
0 0 0 0 0 0 0 X 0 0 0 X X X X X X X 0 0 0 X 0 X X 0 0 0 0 X 0 0 0 X X X 0 0 X 0 X 0 0 X X 0 X 0 X 0 X X X 0 X X 0 X 0 0 0 0 X X X 0 X X 0 X 0 0 0 X 0 0 0 X X 0 X 0 0 0 0 0 X
0 0 0 0 0 0 0 0 X X X 0 0 0 X 0 0 0 X 0 X X X 0 0 0 X 0 X X X X 0 X X 0 0 0 X 0 X 0 0 0 X X X 0 0 0 X X X 0 X X 0 0 X X 0 X 0 0 X 0 X 0 X X X X 0 0 X X 0 0 X X X 0 X X X 0 0
generates a code of length 87 over Z2[X]/(X^2) who´s minimum homogenous weight is 76.
Homogenous weight enumerator: w(x)=1x^0+171x^76+202x^78+463x^80+412x^82+499x^84+402x^86+435x^88+376x^90+357x^92+270x^94+236x^96+108x^98+97x^100+22x^102+29x^104+12x^108+4x^112
The gray image is a linear code over GF(2) with n=174, k=12 and d=76.
This code was found by Heurico 1.16 in 3.96 seconds.