The generator matrix

 1  0  0  1  1  1  X  1  1 X^2  1  1 X^2+X  0 X^2  1  1 X^2+X  1 X^2+X  1  1  1  1  0  X  1  1 X^2  1 X^2  1  1  1  X X^2  X  1  X  1 X^2  0  1  1
 0  1  0  0  1  1  1  X X^2+X+1  1  X X^2+X+1  1  1 X^2+X  1 X^2  1 X+1  X X^2+X+1 X^2+X  X  X  0  1 X+1  1  1  0  1 X+1 X^2  0  1  1  1 X^2+X+1 X^2 X^2  1 X^2+X X^2  0
 0  0  1 X+1 X^2+X+1  0  1  X X^2+1 X^2+1  1  X X^2+X+1  X  1  1  1 X^2  0  1 X^2+X  0  1 X^2  1  X X+1 X^2+X X+1  1 X^2+X+1  X X^2 X+1 X^2+X X^2 X^2+X X^2+X+1  1 X^2+X  0  1  0  0
 0  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0
 0  0  0  0 X^2  0  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0
 0  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  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 X^2 X^2  0  0 X^2  0 X^2  0  0  0  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+96x^38+130x^39+454x^40+354x^41+555x^42+352x^43+476x^44+282x^45+429x^46+236x^47+375x^48+118x^49+127x^50+48x^51+34x^52+14x^53+7x^54+2x^55+2x^56+2x^58+2x^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 0.446 seconds.