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 X X X X X X 1 X 1 X 1 1 X X 1 X 1 1 X 1 X X 0 1 0 X 1 0 0 1 1 0 1 X 1 1 1 1 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 0 X X 0 X 0 X 0 X X X 0 0 X 0 X 0 0 X 0 X X 0 0 0 X 0 0 0 0 0 0 0 0 X X X 0 0
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 X X 0 0 0 X X X X X 0 0 0 0 0 X X 0 0 X X 0 0 0 X 0 0 X 0 0 X 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 0 X X X 0 0 0 0 0 X X 0 X X 0 X 0 0 0 X X X X 0 0 X X X X X 0 X 0 0 0 X 0 0 0
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 X 0 X X X 0 X X X 0 0 0 X X 0 X X 0 0 X X 0 X X X 0 0 X X X 0 X 0 X X 0 0 0
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 0 0 X X X 0 0 0 0 0 X 0 0 X X X 0 X X 0 0 X 0 0 0 X X X X X 0 0 X 0 0 X 0 0 X
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 0 X 0 X X X 0 X X 0 0 X X 0 X 0 X X X X X 0 X X X X 0 0 0 0 0 X 0 X X 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 X 0 0 X 0 0 0 X X 0 X X X 0 X X 0 X 0 X X X X X X 0 0 0 X 0 X 0 0 X 0 0 0 0 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 0 0 X 0 0 0 X 0 X X X 0 X 0 0 0 X 0 0 X X X X X X X 0 0 0 0 X X X 0 X 0 X X
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 0 X X X X X X 0 0 X X X X 0 X X X 0 X X 0 0 X X X X X 0 X X 0 0 0 X 0 0 0 0 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 0 X 0 X X X X 0 X 0 X X 0 X 0 0 0 0 X 0 X 0 X 0 0 0 0 X X X 0 0 0 0 X 0 0 X
generates a code of length 89 over Z2[X]/(X^2) who´s minimum homogenous weight is 74.
Homogenous weight enumerator: w(x)=1x^0+56x^74+127x^76+179x^78+208x^80+265x^82+341x^84+429x^86+498x^88+475x^90+436x^92+322x^94+225x^96+166x^98+115x^100+93x^102+66x^104+43x^106+19x^108+17x^110+8x^112+3x^114+2x^116+1x^120+1x^136
The gray image is a linear code over GF(2) with n=178, k=12 and d=74.
This code was found by Heurico 1.16 in 6.9 seconds.