The generator matrix

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

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+97x^80+224x^82+155x^84+118x^86+124x^88+90x^90+64x^92+28x^94+36x^96+26x^98+19x^100+20x^102+14x^104+4x^106+2x^108+2x^110

The gray image is a linear code over GF(2) with n=174, k=10 and d=80.
This code was found by Heurico 1.16 in 0.303 seconds.