The generator matrix

1 0 0 0 0 0 1 1 1 X 1 1 0 0 0 0 1 X 1 1 1 1 1 X X 1 0 1 0 1 1 X X 0 1 1 1 1 0 0 1 X X 1
0 1 0 0 0 0 0 0 0 0 0 0 X 1 1 1 X+1 1 1 X X 1 0 X 1 1 X X+1 1 X 1 0 1 X 1 X+1 1 1 0 1 X 1 0 0
0 0 1 0 0 0 0 0 X X 1 1 1 X 1 X+1 X+1 X+1 X X+1 1 0 X+1 1 X X+1 1 0 X X 0 1 1 0 0 0 X 1 1 X+1 0 X 1 X
0 0 0 1 0 0 1 X 1 1 0 X+1 1 1 X 1 1 1 X X 1 X+1 1 0 X+1 0 1 1 X+1 1 X+1 0 X 0 X 1 X+1 0 X+1 0 X+1 1 1 1
0 0 0 0 1 0 1 X+1 0 1 X X+1 1 1 X X+1 X+1 0 X+1 1 X+1 X 0 1 0 X+1 X 1 1 X+1 0 X 1 1 X+1 X+1 1 X X+1 X 1 X+1 0 1
0 0 0 0 0 1 X 1 1 X+1 1 X+1 0 X X+1 1 0 0 0 0 X+1 X X X+1 1 1 1 X+1 0 X 1 0 1 X+1 X+1 X X+1 0 1 X X+1 X+1 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+266x^36+366x^38+592x^40+520x^42+684x^44+498x^46+535x^48+334x^50+209x^52+72x^54+16x^56+2x^58+1x^68

The gray image is a linear code over GF(2) with n=88, k=12 and d=36.
This code was found by Heurico 1.10 in 0.531 seconds.