The generator matrix

 1  0  0  0  1  1  1  X  1  1  0  1  1  0  X  1  1  1  0  X  X  0  1  1  1  X  X  1  X  1  1  1  X  0  1  0  1  0  0  0  1  0  X  1  0  1  1  0  1  X  0  X  X  0  1  1  1  1  1  1  X  X  X  1  1  X  1  0  1  X  1  0  0  0  1  0  1  X  1  1  1  1  1  1  0  1  1
 0  1  0  0  0  0  0  0  1  1  1  1 X+1  1  1  X  0  1  X  0  1  1  X  1 X+1  X  1  0  X  1  X X+1  X  1 X+1  1  1  X  1  1  X  1  0  0  1  1  X  1  0  1  1  0  1  1  X  1  1 X+1  1 X+1  1  1  1  X  1  1  0  1  0  1 X+1  1  X  0  X  1 X+1  1  X  X  1  X  X  0  X  1  1
 0  0  1  0  0  1 X+1  1 X+1  1  X  0  0  1  1  X  0 X+1  1  X  1  X X+1  0  1  1  X X+1  1  X  0 X+1  0  1  1  X  X  1  X  1  X  0  1  0 X+1  1  X X+1 X+1  0  1  X  1  0  1  0 X+1  0 X+1  X  X X+1  1  1  0 X+1  1  0  0  1  1  X  0  1  0  1  1 X+1  X  X  0  X X+1  0  1  X  X
 0  0  0  1  1  1  0  1  X X+1  1  1  0 X+1  0  0 X+1  X  0  1 X+1  X  0  0 X+1  1  1 X+1  X X+1  1  X  1 X+1  1  X  1  1  1  0  0  1 X+1  X  1  0 X+1  0  1  X  X  1  X  X  X  1  1  0  X  X X+1  0 X+1  X  X  0  1  0 X+1  1 X+1 X+1  1  0 X+1  1 X+1  1 X+1  0  0  0  1  X X+1  1 X+1
 0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  0  X  X  0  0  0  0  X  X  0  X  X  X  0  0  X  0  X  0  X  X  0  0  0  X  X  0  0  0  X  0  X  X  X  0  X  0  X  0  X  X  0  X  X  0  0  X  X  0  0  X  0  0  X  X  X  0  0  X  X  0
 0  0  0  0  0  X  X  0  X  X  0  X  X  0  0  X  X  0  X  X  X  X  0  0  0  X  X  X  0  0  0  0  X  0  X  X  X  0  0  X  0  X  X  X  X  X  X  0  0  0  X  0  X  X  X  X  0  X  X  0  X  0  0  X  0  X  X  X  0  X  X  X  X  X  X  0  X  X  X  0  X  X  X  0  X  0  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+106x^80+200x^82+176x^84+140x^86+102x^88+74x^90+61x^92+37x^94+36x^96+29x^98+21x^100+23x^102+7x^104+5x^106+2x^108+4x^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 0.314 seconds.