The generator matrix

 1  0  0  1  1  1 X^2+X  1  1 X^2+X X^2+X  1  1  0  1  1  1  1  X  1  0 X^2  1  1 X^2  X  1  0  1  X  1  1  0 X^2+X X^2  1  0  1  1  1  1  1  1  1
 0  1  0  0  1 X+1  1 X^2  0 X^2  1 X^2+1 X^2+1  1 X^2+X  1 X^2+X X^2+1  0 X^2  1  1 X^2+X  0  X  1 X+1  1 X+1  X X^2+X  1  1  1  1 X^2+1  1 X+1  X X^2+X+1 X^2+X  X  0 X^2
 0  0  1  1  1  0 X+1  X X^2+X+1  1  0 X^2 X+1 X+1 X^2 X+1  1  X  1  X X+1  0  X X+1  1 X^2 X^2 X^2+1 X^2+X  1 X^2+1 X^2+X X^2+X+1  1 X^2+X X+1  X X^2+X+1 X^2+X+1 X^2+X X+1 X^2 X+1 X^2
 0  0  0  X  0 X^2  0 X^2 X^2+X  0 X^2  0  0  0  0  X X^2 X^2+X X^2+X  X X^2+X  X  X X^2 X^2+X  X X^2+X X^2+X X^2+X X^2+X  X X^2  X  X X^2+X X^2+X  X  X X^2  0 X^2+X  X  0  X
 0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  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  0  0 X^2 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+76x^38+200x^39+300x^40+464x^41+429x^42+424x^43+481x^44+416x^45+424x^46+284x^47+219x^48+168x^49+79x^50+72x^51+21x^52+8x^53+14x^54+12x^55+2x^56+2x^58

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 0.459 seconds.