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 1 X 1 0 0 X 0 1 1 X X 1 1 1 X X X 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 0 X 0 0 0 0 X X X 0 X X 0 X 0 X 0 X 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 X X 0 0 0 X X X X X 0 0 0 0 X 0 0 0 0 0 0 0 X 0 0 X X 0 X X X X X
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 X 0 0 X X X X X X 0 0 0 0 X X 0 X X 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 0 X 0 X X 0 0 X 0 0 0 X 0 0 0 0 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 0 0 X X X 0 0 0 0 0 X 0 0 X X X 0 X 0 X 0 X 0 0 X X 0 0 0 X 0 X 0 X 0 0 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 0 X 0 X X X 0 X X 0 0 X X 0 X X 0 0 0 X X X 0 0 X X X X 0 0 0 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 X 0 0 X 0 0 0 X X 0 X X X 0 X X 0 X X 0 0 X X 0 0 0 X 0 X 0 0 0 X 0 X 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 0 0 X 0 0 0 X 0 X X X 0 X 0 0 0 X 0 0 X X X 0 X X X 0 X X 0 0 X X X 0 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 0 X X X X X X 0 0 X X X X 0 X X X 0 X X 0 X X 0 X 0 0 X X X 0 X 0 0 0 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 0 X 0 X X X X 0 X 0 X X 0 X 0 0 0 X 0 X X 0 0 0 0 X X 0 X 0 X 0 0 0 X 0
generates a code of length 87 over Z2[X]/(X^2) who´s minimum homogenous weight is 72.
Homogenous weight enumerator: w(x)=1x^0+103x^72+6x^74+317x^76+74x^78+431x^80+174x^82+563x^84+350x^86+641x^88+274x^90+446x^92+118x^94+284x^96+26x^98+173x^100+2x^102+72x^104+33x^108+4x^112+3x^116+1x^132
The gray image is a linear code over GF(2) with n=174, k=12 and d=72.
This code was found by Heurico 1.16 in 6.34 seconds.