The generator matrix

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

generates a code of length 87 over Z2[X]/(X^2) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+94x^80+206x^82+178x^84+138x^86+114x^88+76x^90+56x^92+44x^94+29x^96+26x^98+20x^100+18x^102+16x^104+4x^106+2x^108+2x^112

The gray image is a linear code over GF(2) with n=174, k=10 and d=80.
This code was found by Heurico 1.10 in 0.078 seconds.