The generator matrix

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

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+7x^40+28x^41+18x^42+14x^44+24x^45+12x^46+8x^48+12x^49+2x^50+1x^52+1x^76

The gray image is a linear code over GF(2) with n=88, k=7 and d=40.
This code was found by Heurico 1.16 in 0.016 seconds.