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  X  X  1  X  1  X  X  1  X  0  1  1  X  1  X  1  1  1  1  1  X  1  1  X  1  1  1  X  1  1  0  1  0  1  0  1  1  0  1  X  X  1  1  X  X  1  1
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  0  0  X  X  X  0  X  X  0  0  X  0  0  X  X  0  0  0  X  X  X  0  X  0  X  X  X  X  0  X  X  0  0  0  0  X  X  X  0  X  X  X  0  X  0  0  0  0  0  0  X  0  X  0  X  0  X  X  X  X  0  0  0
 0  0  X  0  0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  X  X  0  0  0  0  0  0  0  0  X  0  X  X  X  X  X  X  X  0  0  X  0  0  X  X  X  0  0  X  0  0  X  X  0  0  X  X  0  X  0  0  X  X  0  X  0  X  X  X  X  X  X  X  X  0  0  X  X  0  X  X  X  X  X  0  0
 0  0  0  X  0  0  0  0  0  0  0  0  X  X  X  X  X  0  X  X  X  X  0  0  X  X  X  X  X  X  0  X  0  X  X  0  X  0  0  X  X  0  X  0  X  0  X  0  0  X  X  0  0  X  X  X  0  0  X  0  0  X  0  0  0  0  0  0  0  0  X  0  0  X  0  X  0  0  X  X  0  0  0  X  0  0
 0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  0  X  X  X  0  X  0  X  0  X  0  0  X  0  X  0  0  0  0  0  X  X  0  0  X  0  X  X  X  X  0  0  0  X  X  0  0  X  X  0  0  X  X  X  X  0  0  0  0  X  X  X  X  0  X  X  X  0  X  0  0  X  0  X  X  X  0  X  0  0  0
 0  0  0  0  0  X  0  0  0  0  0  X  0  0  X  X  X  X  X  0  0  X  X  0  0  0  X  0  0  0  X  X  0  X  X  0  X  X  X  0  0  0  X  0  X  X  X  X  X  X  X  X  0  X  0  X  X  X  X  X  0  X  X  0  X  X  X  X  0  0  X  0  X  X  0  X  X  0  0  0  0  0  X  0  0  0
 0  0  0  0  0  0  X  0  0  0  X  0  0  0  X  X  0  0  X  0  0  X  X  0  X  X  X  0  X  X  X  0  0  0  0  X  X  0  X  0  X  0  0  0  X  0  0  0  X  X  0  0  X  0  X  X  X  0  0  X  0  X  0  X  X  0  0  X  X  0  X  0  X  0  X  0  0  X  X  0  0  0  0  X  0  0
 0  0  0  0  0  0  0  X  0  0  X  0  0  X  0  0  X  0  0  X  0  X  X  X  0  X  0  X  X  X  0  X  X  0  X  0  0  X  0  X  0  0  X  X  X  X  0  X  0  0  X  0  X  X  0  X  0  0  0  X  X  0  0  X  X  X  X  X  0  0  X  X  X  X  0  0  0  0  X  X  X  0  0  0  0  0
 0  0  0  0  0  0  0  0  X  0  X  X  X  X  0  0  0  0  X  0  0  0  0  X  X  0  0  X  X  0  X  0  X  0  0  X  0  0  X  0  X  X  0  X  0  X  X  X  0  0  X  0  X  0  X  0  X  0  0  0  X  0  X  X  X  0  0  X  0  X  X  0  X  0  X  0  0  X  0  X  0  0  X  0  0  0
 0  0  0  0  0  0  0  0  0  X  X  X  X  0  0  X  X  X  X  X  0  X  X  X  X  0  X  0  X  X  X  0  X  0  X  0  X  0  0  X  0  X  0  X  0  X  X  X  0  0  0  X  0  X  X  X  0  X  0  0  0  0  0  0  0  0  X  X  0  X  X  0  X  X  0  0  X  X  X  0  X  X  0  0  0  0

generates a code of length 86 over Z2[X]/(X^2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+77x^72+2x^74+155x^76+40x^78+269x^80+130x^82+296x^84+176x^86+306x^88+118x^90+204x^92+40x^94+114x^96+6x^98+63x^100+28x^104+17x^108+4x^112+1x^120+1x^132

The gray image is a linear code over GF(2) with n=172, k=11 and d=72.
This code was found by Heurico 1.16 in 1.47 seconds.