The generator matrix

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

generates a code of length 88 over Z2[X]/(X^2) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+344x^80+564x^84+482x^88+294x^92+185x^96+120x^100+42x^104+14x^108+2x^112

The gray image is a linear code over GF(2) with n=176, k=11 and d=80.
This code was found by Heurico 1.10 in 73.2 seconds.