The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  X  1  1  1  1  X  1  1  X  1  X  X  X  X  1
 0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2
 0  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0  0  0  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0
 0  0  0 X^2  0  0  0  0 X^2  0  0 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2
 0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0
 0  0  0  0  0 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0
 0  0  0  0  0  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0  0  0  0 X^2  0  0
 0  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0

generates a code of length 44 over Z2[X]/(X^3) who�s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+66x^38+104x^40+50x^42+582x^44+112x^46+65x^48+6x^50+2x^52+20x^54+13x^56+2x^62+1x^72

The gray image is a linear code over GF(2) with n=176, k=10 and d=76.
This code was found by Heurico 1.16 in 34.9 seconds.