The generator matrix

 1  0  0  0  0  1  1  1  X  1  1  X  X  X  0  0  1  1  1  0  1  0  1  X  1  1  0  1  1  1  0  X  1  0  X  1  1  0  0  0  X  1  0  1
 0  1  0  0  0  0  0  0  0  1  1  1  0  1  1  X  1  1  X  X X+1  1  0  1 X+1  X  1 X+1 X+1  0  X  1  1  X  1  1 X+1  1  X  1  1  0  1  0
 0  0  1  0  0  0  1  1  1  1 X+1  0  1  0  X  1  X  0 X+1  0  X X+1  0  1  X X+1  0  1  1 X+1  X  1  X  1 X+1 X+1  0  0  1  X  0  X  0  0
 0  0  0  1  0  1  1  X X+1  0 X+1  1  1  X  1  0  X X+1 X+1  1  1  X  0 X+1  0  X  1  X  0  X  1  1  X  0  0  1  0 X+1  X  1  1  0  X  0
 0  0  0  0  1  1  X X+1  1  0  1  1  0 X+1  0 X+1  0  1 X+1  1  X  1 X+1 X+1 X+1  0  X  X  1  0  1 X+1  X X+1  1  0  X  0  X X+1  1  0  X  0
 0  0  0  0  0  X  0  X  0  X  0  0  X  X  X  X  0  X  X  0  X  0  X  X  X  X  0  0  0  0  X  0  X  0  X  0  0  X  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+55x^36+94x^37+107x^38+138x^39+158x^40+150x^41+149x^42+162x^43+148x^44+122x^45+115x^46+142x^47+115x^48+114x^49+81x^50+54x^51+55x^52+32x^53+26x^54+16x^55+10x^56+2x^58+2x^60

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 0.325 seconds.