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.