The generator matrix

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

generates a code of length 90 over Z2[X]/(X^2) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+223x^80+392x^82+504x^84+444x^86+455x^88+406x^90+374x^92+298x^94+304x^96+232x^98+234x^100+106x^102+63x^104+32x^106+16x^108+8x^110+2x^112+2x^114

The gray image is a linear code over GF(2) with n=180, k=12 and d=80.
This code was found by Heurico 1.10 in 52.7 seconds.