The generator matrix

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

generates a code of length 44 over Z2[X]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+19x^40+44x^41+40x^42+36x^43+28x^44+24x^45+16x^46+12x^47+11x^48+4x^49+4x^50+2x^52+4x^53+4x^54+1x^56+4x^57+2x^60

The gray image is a linear code over GF(2) with n=88, k=8 and d=40.
This code was found by Heurico 1.10 in 0 seconds.