The generator matrix

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

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+222x^36+450x^38+554x^40+558x^42+595x^44+572x^46+503x^48+344x^50+206x^52+58x^54+30x^56+2x^58+1x^60

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 3.26 seconds.