The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  0  0  X  1  X  1  1  1  0  0  1  1  1  1  1  X  X  X  0  1  1  0  X  1  1  0  0  0  X  1  X  1
 0  1  0  0  0  1  1  1  X  0  1 X+1  1  1  1 X+1  X  0  0  1  X  1  X  1  0  X X+1  0  1  0  X  0  0  1  X  0  X  X  1  1  1 X+1  X  0
 0  0  1  0  1  1  0  1  0 X+1  X  1  X  1  0  X  1  1  X X+1  1  1  1  1 X+1  1  X  1  X  1  1  0 X+1 X+1  0  0 X+1  1  1  1 X+1  1  1  1
 0  0  0  1  1  0  1 X+1  1  X  0 X+1  1  X  1  1 X+1  0  1  X  0  X X+1 X+1  0  X X+1 X+1  0 X+1 X+1  X X+1  0  1  X X+1  1  0  1 X+1  0  1  1
 0  0  0  0  X  0  0  X  0  X  X  X  0  0  X  X  0  X  0  X  X  0  X  0  0  0  0  0  X  X  0  0  X  X  0  X  X  0  X  0  0  X  X  0
 0  0  0  0  0  X  0  0  0  0  X  0  0  X  X  X  0  0  X  X  X  0  X  0  0  X  X  0  0  X  X  X  X  X  X  X  0  X  0  0  X  X  X  0
 0  0  0  0  0  0  X  0  0  0  0  X  X  X  X  X  X  X  0  X  X  0  X  X  X  0  X  0  0  0  X  X  0  0  0  X  X  0  X  0  X  0  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+52x^36+74x^37+110x^38+172x^39+147x^40+124x^41+156x^42+152x^43+135x^44+172x^45+137x^46+112x^47+118x^48+112x^49+87x^50+72x^51+49x^52+26x^53+19x^54+4x^55+10x^56+4x^57+1x^58+2x^62

The gray image is a linear code over GF(2) with n=88, k=11 and d=36.
This code was found by Heurico 1.16 in 0.336 seconds.