The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  X  X  1  1  X  X  1  0  1  0  1  1  X  1  1  1  1  1  0  1  0  X  0  1  1  0  1  X  0  1  1  1
 0  1  0  1  0  1  1  0  0  1 X+1  1  1  X  0  1  1  1  X  1 X+1  0  0 X+1  1  1  0  X X+1  X  X  0  X  1  1  1  1  1  1  X  X X+1  0  0
 0  0  1  1  1  0  1  0  1  1  0  X  1  1  0 X+1  1 X+1  1  0  0  1  X X+1  X  1  X  1  0  1  1  0  1  1 X+1 X+1  0  1  1  1  1  0  0  0
 0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  X  X  X  0  X  0  X  0  0  X  X  X  0  0  0  X  X  X  X  0  0  X  0  0  X  X  0  0  0
 0  0  0  0  X  0  0  0  0  0  X  X  0  X  X  0  X  0  0  X  0  0  X  X  0  0  X  X  0  0  0  X  0  X  X  0  X  X  X  X  0  0  0  0
 0  0  0  0  0  X  0  0  0  0  X  0  X  0  X  X  0  X  0  X  0  0  0  0  0  X  X  X  0  X  0  X  0  X  0  X  0  0  X  0  0  X  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  X  0  0  0  X  X  0  X  X  0  X  X  X  0  0  X  0  X  0  0  0  X  0  0  X  X  0  X  X  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  0  X  X  0  X  X  0  0  X  0  X  X  X  X  X  X  X  X  X  X  0  0
 0  0  0  0  0  0  0  0  X  0  X  X  X  X  0  X  X  X  X  X  0  0  0  0  X  X  0  0  X  X  0  X  X  0  0  0  0  X  X  0  X  X  0  0
 0  0  0  0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  X  X  X  X  X  0  X  X  0  X  X  X  0  X  0  0  0  X  0  X  0  0  X  X  0  0

generates a code of length 44 over Z2[X]/(X^2) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+86x^32+166x^34+462x^36+604x^38+952x^40+1164x^42+1354x^44+1048x^46+1123x^48+510x^50+504x^52+92x^54+110x^56+15x^60+1x^76

The gray image is a linear code over GF(2) with n=88, k=13 and d=32.
This code was found by Heurico 1.16 in 5.47 seconds.