The generator matrix

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

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+278x^80+350x^84+188x^88+88x^92+49x^96+54x^100+12x^104+4x^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 33.9 seconds.