The generator matrix

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

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+53x^40+48x^42+76x^44+48x^46+13x^48+2x^52+13x^56+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 1.16 in 0.0162 seconds.