The generator matrix

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

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+109x^36+546x^37+910x^38+1464x^39+2096x^40+2836x^41+2940x^42+3530x^43+3609x^44+3756x^45+3307x^46+2872x^47+1931x^48+1392x^49+774x^50+354x^51+156x^52+122x^53+33x^54+20x^55+2x^56+4x^57+4x^58

The gray image is a linear code over GF(2) with n=176, k=15 and d=72.
This code was found by Heurico 1.13 in 8.25 seconds.