The generator matrix

 1  0  1  1  1 X^2  1  1  0  0  1  1  1  0  1  1 X^2  1  1  1  0  1  1 X^2+X  1  1  1  X X^2+X X^2  1  1  1  0  0  1  1  1 X^2  X  X  1  1  1
 0  1  1  0  1  1 X^2 X+1  1  1 X^2 X^2+X+1 X^2  1 X^2  1  1 X^2+X+1 X^2 X^2  1  1 X^2+1  1  X X^2+1 X^2+X  1  1  1  1  1 X^2  1  1  1  X X^2+X+1  1 X^2+X  1  X  0 X^2
 0  0  X  0  0  0  0 X^2 X^2+X  X X^2+X X^2+X X^2+X X^2 X^2+X  X X^2+X  0  X X^2  0 X^2+X  0 X^2+X  X  X  X X^2 X^2+X X^2 X^2  X  0  X X^2  X X^2+X  0 X^2  X  0  0 X^2+X X^2
 0  0  0  X  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2+X X^2+X  X  X  X  X X^2+X  X  X X^2+X X^2 X^2  0 X^2  X X^2  X  X X^2+X X^2+X  X X^2+X X^2+X  0  X X^2 X^2 X^2 X^2  X  X
 0  0  0  0  X X^2+X X^2+X X^2  X  0  0 X^2+X  X  X X^2+X X^2+X  X X^2 X^2 X^2+X  0 X^2  X X^2+X  0  X  X X^2+X  X  0  X X^2+X  0 X^2  0 X^2  0  0 X^2 X^2  X  X X^2+X 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+154x^38+100x^39+418x^40+312x^41+496x^42+348x^43+503x^44+368x^45+516x^46+316x^47+283x^48+88x^49+80x^50+4x^51+64x^52+34x^54+10x^56+1x^60

The gray image is a linear code over GF(2) with n=176, k=12 and d=76.
This code was found by Heurico 1.16 in 0.565 seconds.