The generator matrix

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

generates a code of length 86 over Z2[X]/(X^2) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+275x^80+353x^84+179x^88+106x^92+60x^96+21x^100+21x^104+8x^108

The gray image is a linear code over GF(2) with n=172, k=10 and d=80.
This code was found by Heurico 1.16 in 7.07 seconds.