The generator matrix

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

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+25x^36+24x^37+64x^38+52x^39+78x^40+108x^41+77x^42+92x^43+61x^44+68x^45+63x^46+76x^47+58x^48+52x^49+34x^50+36x^51+23x^52+4x^53+14x^54+6x^56+1x^58+3x^60+3x^62+1x^64

The gray image is a linear code over GF(2) with n=88, k=10 and d=36.
This code was found by Heurico 1.16 in 0.112 seconds.