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

generates a code of length 88 over Z2[X]/(X^2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+105x^72+247x^76+36x^78+366x^80+168x^82+539x^84+316x^86+644x^88+304x^90+505x^92+156x^94+307x^96+40x^98+190x^100+4x^102+99x^104+52x^108+14x^112+2x^116+1x^132

The gray image is a linear code over GF(2) with n=176, k=12 and d=72.
This code was found by Heurico 1.16 in 6.35 seconds.