The generator matrix

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

generates a code of length 90 over Z2[X]/(X^2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+200x^78+449x^80+741x^82+795x^84+796x^86+865x^88+818x^90+788x^92+701x^94+682x^96+511x^98+373x^100+260x^102+129x^104+66x^106+12x^108+3x^110+2x^112

The gray image is a linear code over GF(2) with n=180, k=13 and d=78.
This code was found by Heurico 1.10 in 4.63 seconds.