The generator matrix

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

generates a code of length 44 over Z2[X]/(X^2) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+104x^38+229x^40+182x^42+133x^44+80x^46+112x^48+94x^50+65x^52+20x^54+2x^56+2x^60

The gray image is a linear code over GF(2) with n=88, k=10 and d=38.
This code was found by Heurico 1.10 in 0.047 seconds.