The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X X 0 X X X X X X 0 X 1 0 1 1 0 1 1 1 1 0 1 1 0 1 X 1 1 X 0 0 0 1
0 X 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X X X X X X X 0 X X X X 0 X 0 0 0 X X X 0 X X X 0 X X X X X X X X X 0 0 X X X X 0 X 0 X X X X 0 X X 0 X X 0 0 0 0 0 X 0 0 X X 0 0 X
0 0 X 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 X X X X X X X 0 0 0 X 0 0 0 X X X 0 0 0 X X X 0 X X 0 0 X X X 0 0 0 X 0 0 0 0 X X 0 X 0 0 X 0 X X X X X 0 0 X X X 0 0 X 0 0 0 0 X X 0 0 0 X 0
0 0 0 X 0 0 0 0 0 0 0 0 0 X 0 0 0 X X X X X X 0 0 0 0 X 0 X X X 0 X 0 0 X X 0 0 0 X X X 0 X 0 X X 0 X 0 0 X X 0 X X X 0 0 X X 0 0 0 0 0 0 X X X 0 X X 0 0 X X X X X 0 0 0 X 0 0 X X
0 0 0 0 X 0 0 0 0 0 0 0 0 X 0 X X X X X X 0 X X 0 X X X 0 0 0 X X X X X 0 X X 0 0 0 X 0 0 0 0 X 0 X 0 0 X 0 X 0 0 X X X X X X X X X X X X X 0 0 0 0 0 X X 0 0 X X 0 X 0 X 0 0 0 X X
0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 X X 0 X X 0 X 0 X 0 X X X X 0 0 X X 0 0 0 X 0 X 0 0 0 0 X X 0 X X X 0 X 0 0 0 0 X 0 X X 0 0 0 X 0 X X X X X 0 X 0 0 X X 0 0 0 X X 0 0 0 X 0 X X 0 X 0
0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 0 X X X X 0 X X 0 X 0 X 0 0 X 0 0 X X X 0 0 0 0 X 0 0 0 X X X X 0 X X X X X X 0 X X X 0 0 0 0 0 0 X 0 0 0 0 0 X X X X X X X 0 X X 0 X 0 0 X 0 X X 0 0
0 0 0 0 0 0 0 X 0 0 0 X 0 0 0 0 X X 0 X 0 0 0 X X X 0 0 X 0 X X X X 0 0 0 X X X X X 0 0 0 0 X X X X 0 0 X X 0 0 X 0 0 X X 0 0 X 0 X 0 0 X X X 0 0 0 X 0 X X X X 0 X 0 0 0 0 X 0 X 0
0 0 0 0 0 0 0 0 X 0 0 X 0 0 0 X 0 0 X 0 X 0 0 X 0 0 0 0 X X X 0 0 X X 0 X X X X 0 0 0 X X X X 0 X 0 0 X X X 0 0 X X 0 X 0 X X X 0 0 0 X 0 0 X X 0 X X X 0 0 0 0 X 0 0 X 0 X X 0 X 0
0 0 0 0 0 0 0 0 0 X 0 X X X X X 0 0 0 X 0 0 X X 0 0 X 0 X X 0 0 X X 0 X X 0 0 0 0 X 0 0 0 X 0 X X 0 X X 0 0 X 0 0 X 0 0 X X X 0 X 0 X 0 X 0 X 0 X X 0 0 0 X 0 X 0 0 0 X X 0 0 X X X
0 0 0 0 0 0 0 0 0 0 X X X X X 0 0 X X X X X 0 X 0 X 0 0 0 0 0 X 0 X 0 0 X 0 X X 0 0 0 X 0 0 X 0 0 X X X 0 0 0 0 X 0 0 X X X 0 X X 0 X 0 0 X 0 X 0 X 0 X 0 X X 0 0 X X 0 0 X 0 0 X X
generates a code of length 90 over Z2[X]/(X^2) who´s minimum homogenous weight is 76.
Homogenous weight enumerator: w(x)=1x^0+186x^76+18x^78+330x^80+82x^82+487x^84+224x^86+591x^88+372x^90+559x^92+226x^94+420x^96+90x^98+263x^100+12x^102+144x^104+63x^108+17x^112+10x^116+1x^136
The gray image is a linear code over GF(2) with n=180, k=12 and d=76.
This code was found by Heurico 1.16 in 14.3 seconds.