The generator matrix

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

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+124x^38+245x^40+456x^42+520x^44+354x^46+173x^48+102x^50+48x^52+18x^54+4x^56+2x^58+1x^72

The gray image is a linear code over GF(2) with n=176, k=11 and d=76.
This code was found by Heurico 1.16 in 0.213 seconds.