The generator matrix

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

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+126x^38+178x^40+211x^42+134x^44+81x^46+121x^48+77x^50+70x^52+17x^54+8x^56

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 0.101 seconds.