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  X  X  1  1  1  1  1  X  1  1  1  X  1  1  1  X  1
 0  X  0  0  0  0  0  0  0  0  X  X  0  0  0  X  0  0  0  0  X  X  X  X  0  X  X  X  X  0  X  X  0  X  X  X  0  0  0  0  0  0  X  0
 0  0  X  0  0  0  0  0  0  X  X  X  0  X  X  0  0  0  X  X  X  X  X  X  0  X  0  0  0  0  0  0  X  X  X  0  X  0  X  0  X  0  X  0
 0  0  0  X  0  0  0  0  0  X  0  X  X  X  0  X  0  X  X  0  0  0  0  0  X  0  X  X  0  X  0  X  X  0  X  0  0  X  0  X  0  X  0  0
 0  0  0  0  X  0  0  0  X  0  0  X  X  0  X  X  0  0  X  X  0  0  0  X  X  X  X  0  0  0  X  X  0  0  X  0  X  X  X  0  0  0  0  0
 0  0  0  0  0  X  0  0  X  0  X  0  0  X  X  X  0  X  X  0  0  0  0  X  X  0  0  X  X  X  0  0  0  X  X  0  X  0  0  0  X  0  X  0
 0  0  0  0  0  0  X  0  X  X  X  0  0  0  X  X  X  0  0  X  0  0  X  0  X  0  X  X  0  X  X  0  0  0  0  X  0  X  0  X  0  X  0  0
 0  0  0  0  0  0  0  X  X  X  0  0  X  X  X  0  X  0  X  0  0  X  X  0  0  0  X  X  0  0  0  X  0  X  X  0  X  0  0  0  X  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+32x^36+25x^38+8x^39+35x^40+40x^41+31x^42+80x^43+30x^44+80x^45+27x^46+40x^47+17x^48+8x^49+20x^50+10x^52+19x^54+3x^56+5x^58+1x^78

The gray image is a linear code over GF(2) with n=88, k=9 and d=36.
This code was found by Heurico 1.16 in 0.032 seconds.