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

generates a code of length 44 over Z2[X]/(X^3) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+104x^36+16x^37+202x^38+76x^39+394x^40+144x^41+538x^42+316x^43+676x^44+176x^45+502x^46+228x^47+323x^48+48x^49+190x^50+20x^51+82x^52+40x^54+18x^56+2x^60

The gray image is a linear code over GF(2) with n=176, k=12 and d=72.
This code was found by Heurico 1.16 in 0.731 seconds.