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

generates a code of length 92 over Z2[X]/(X^2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+116x^72+71x^74+341x^76+250x^78+470x^80+379x^82+16x^83+569x^84+144x^85+454x^86+576x^87+554x^88+1344x^89+555x^90+2016x^91+604x^92+2016x^93+615x^94+1344x^95+543x^96+576x^97+601x^98+144x^99+448x^100+16x^101+522x^102+266x^104+384x^106+143x^108+195x^110+34x^112+56x^114+7x^116+11x^118+2x^122+1x^166

The gray image is a linear code over GF(2) with n=184, k=14 and d=72.
This code was found by Heurico 1.16 in 97.1 seconds.