The generator matrix

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

generates a code of length 88 over Z2[X]/(X^2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+242x^78+379x^80+426x^82+522x^84+410x^86+419x^88+408x^90+340x^92+282x^94+240x^96+174x^98+110x^100+90x^102+33x^104+16x^106+4x^108

The gray image is a linear code over GF(2) with n=176, k=12 and d=78.
This code was found by Heurico 1.10 in 179 seconds.