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

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+60x^38+86x^40+233x^42+281x^44+226x^46+71x^48+52x^50+6x^52+2x^54+2x^56+3x^58+1x^76

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 0.09 seconds.