The generator matrix

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

generates a code of length 44 over Z2[X]/(X^2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+232x^36+462x^38+551x^40+504x^42+583x^44+594x^46+538x^48+384x^50+152x^52+68x^54+22x^56+4x^58+1x^68

The gray image is a linear code over GF(2) with n=88, k=12 and d=36.
This code was found by Heurico 1.16 in 1.45 seconds.