The generator matrix

 1  0  0  0  0  1  1  1  0  X  1  1  X  1  1  0  1  1  0  1  X  X  X  0  1  1  1  1  X  X  1  0  1  1  1  1  X  1  0  X  1  1  X  1
 0  1  0  0  0  X  X  X  X  1  1  1  1 X+1  0  1  0  X  X X+1  0  1  1  1 X+1 X+1  0 X+1  0  0 X+1  X  0 X+1 X+1  X  1  1  0  0 X+1 X+1  1  0
 0  0  1  0  0  0  0  X  0  0  X  X  0 X+1 X+1 X+1  1 X+1  1  1  1 X+1 X+1  X  1  X  1  0  X  1  0  1  1  X  X  1  X  0  1  1  X  1  1 X+1
 0  0  0  1  0  0 X+1 X+1  1  X  0  1  1  0  1  0 X+1  X  1  1  1 X+1  1 X+1  X  X  X X+1  1  0  1 X+1  0  X  1 X+1 X+1  X  1  0 X+1  0  1  0
 0  0  0  0  1  1 X+1  X X+1 X+1  1  0  X  X X+1  X  X  1  0  X X+1 X+1  0  1 X+1  0  0  1  0 X+1  0  0  1  X X+1  1  X  0  X  1  X X+1  0  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+106x^38+213x^40+198x^42+122x^44+106x^46+115x^48+76x^50+50x^52+24x^54+11x^56+2x^58

The gray image is a linear code over GF(2) with n=88, k=10 and d=38.
This code was found by Heurico 1.16 in 0.0904 seconds.