The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  X  1  1  1  1  0  1  X  1  1  1  0  1  1  0  1  X  1  1  X  1  0  1  1  1  1  1  1  1  0  1  X  1  1  0  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  0  X  1  0  1  0  1  X  0  1  1  X
 0  1  1  0  1  1  0  1  1  X X+1  1  1  0 X+1 X+1  0  1  X  1 X+1 X+1  0  1  0 X+1  1 X+1  1  X  0  1 X+1  1  0 X+1 X+1  1 X+1  1  0  1  X  1  0  0  1  1  1  1 X+1 X+1  1  1 X+1  1 X+1 X+1 X+1  1  1  1 X+1  X X+1 X+1  1 X+1  1  1  1 X+1  1 X+1  X  0  1  1  X  0  1  0  1  1  1  1  X  0
 0  0  X  0  0  0  0  0  0  0  X  0  0  X  X  0  0  X  X  X  X  X  X  X  0  0  0  0  X  X  0  X  0  0  X  X  X  0  X  X  0  0  X  X  X  X  X  X  X  0  0  0  X  0  0  X  0  X  X  X  X  X  0  0  X  X  X  0  X  0  X  0  0  X  X  0  0  0  0  0  0  0  0  0  X  X  0  0
 0  0  0  X  0  0  0  0  0  X  0  0  0  X  X  X  X  0  0  0  0  X  X  X  X  0  X  0  0  X  X  X  X  0  X  0  X  0  0  0  0  0  X  X  X  X  0  0  0  X  0  0  0  X  X  0  0  X  X  0  X  0  X  X  X  0  0  X  X  X  0  0  0  X  X  0  X  0  0  X  0  0  X  X  0  X  X  X
 0  0  0  0  X  0  0  0  0  0  X  X  X  0  0  X  X  0  X  0  X  X  X  X  X  X  0  X  X  X  X  X  X  X  0  X  X  0  X  0  X  X  0  0  0  X  0  X  X  X  0  0  0  0  0  X  X  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  0  0  0  0  0  0  0  0  X  0  0  0  0  X  0  X
 0  0  0  0  0  X  0  0  X  0  0  X  0  0  X  X  0  X  0  0  0  X  X  X  0  X  X  0  X  0  X  X  0  X  X  0  0  0  X  0  0  0  X  X  0  0  X  X  0  X  0  X  0  0  0  X  X  0  X  0  0  X  X  X  0  X  X  X  0  0  X  X  0  0  X  X  0  0  X  0  0  X  X  0  0  X  X  X
 0  0  0  0  0  0  X  0  X  X  0  0  X  0  X  X  X  X  X  X  0  X  X  X  0  X  0  X  X  0  0  0  0  X  0  X  0  X  X  X  0  0  X  X  X  X  0  0  0  X  X  X  X  0  0  0  0  X  0  0  0  0  0  0  X  0  0  0  X  X  X  0  0  0  0  0  X  X  X  0  0  X  0  0  0  X  X  0
 0  0  0  0  0  0  0  X  X  0  X  0  X  0  0  X  0  X  0  X  0  X  0  0  X  X  0  0  0  X  X  0  0  0  X  X  0  X  X  0  X  X  X  X  0  0  0  0  X  X  0  X  X  0  X  0  X  0  0  X  0  X  X  0  X  0  X  0  0  X  X  0  0  X  0  X  0  X  0  X  X  0  X  X  0  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+140x^80+60x^82+209x^84+68x^86+137x^88+76x^90+140x^92+44x^94+95x^96+8x^98+31x^100+5x^104+2x^108+4x^112+2x^116+2x^128

The gray image is a linear code over GF(2) with n=176, k=10 and d=80.
This code was found by Heurico 1.16 in 0.414 seconds.