The generator matrix

1 0 0 0 0 1 1 1 X 1 1 0 0 1 X 1 1 X 0 1 X 1 1 X 1 1 1 1 0 X X 0 0 X 1 1 0 0 1 0 1 1 1 1
0 1 0 0 0 0 0 0 0 1 1 1 0 1 1 X X+1 X 0 X+1 1 X X+1 1 X 1 X+1 X 1 1 0 1 X 0 1 X+1 1 1 X X 0 X 0 0
0 0 1 0 0 0 1 1 1 0 X X 1 X 0 X+1 1 X 1 X+1 1 0 1 X 0 1 X+1 X X X+1 X 1 1 X X X 0 0 1 X X+1 X X+1 0
0 0 0 1 0 1 0 X+1 1 1 0 X+1 1 0 0 X+1 X 1 X X+1 X+1 X+1 0 X X 1 X X+1 0 1 1 X+1 1 1 1 X+1 X+1 1 X+1 1 X X+1 1 X+1
0 0 0 0 1 1 X+1 X 1 X 1 1 0 0 X+1 X+1 1 X+1 1 X+1 1 0 0 0 1 X 1 X X X 0 X 1 0 1 1 1 X+1 0 X+1 0 X+1 X X+1
0 0 0 0 0 X X 0 0 0 0 X X X 0 0 X 0 0 X X X 0 X X X 0 0 0 X 0 0 X X X 0 0 X 0 0 0 X X 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+36x^36+90x^37+109x^38+148x^39+148x^40+170x^41+176x^42+138x^43+139x^44+132x^45+139x^46+110x^47+126x^48+116x^49+63x^50+70x^51+57x^52+34x^53+24x^54+14x^55+5x^56+2x^57+1x^58

The gray image is a linear code over GF(2) with n=88, k=11 and d=36.
This code was found by Heurico 1.10 in 0.125 seconds.