The generator matrix

 1  0  0  0  1  1  1  0  1  X  X X^2+X  1  1  1  1  X  1  1  X  1 X^2+X  X  1  0  1  X  0 X^2  1  1  0  X  1 X^2 X^2  1  0  0  1  1  X  1  1
 0  1  0  0  0  1  1  1 X^2 X^2+X  1  1 X^2 X^2+1 X^2+X+1 X^2  1 X^2+X  X X^2+X X^2 X^2+X  1 X^2+X+1  1 X+1  0  0  X  1 X+1  1  1 X+1  1 X^2 X^2+1  X X^2 X^2+X+1 X^2  1  0  0
 0  0  1  0  1  1 X^2 X^2+1 X^2+X+1  1 X^2  1  X X^2+1  0 X^2+1 X^2+X+1  1 X^2 X^2+X X^2  1  0 X^2+X X^2+X+1 X^2+1  1  1 X^2  X X^2  1 X^2+X+1 X^2+X+1 X^2+X  1  1  1 X^2 X^2 X^2+X+1  X X+1  0
 0  0  0  1  1  0 X^2+1  1 X^2  1 X+1  X X+1  1 X^2 X+1  X  0  1  1  0 X^2+X+1 X^2 X^2+X+1 X+1 X^2+X+1 X^2+X X+1  1 X^2+X+1  0 X^2+X+1 X^2+X X^2+X+1 X^2+X+1 X^2+X X^2 X^2+X+1  1  X X^2+1 X^2+1  1  X
 0  0  0  0  X  0  0  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2  X  X X^2+X  X X^2+X X^2+X  X  X  X X^2 X^2 X^2 X^2+X X^2+X  X  0  0  X  0  X  X X^2  X  X X^2+X  X
 0  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0 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 36.

Homogenous weight enumerator: w(x)=1x^0+190x^36+392x^37+1220x^38+1224x^39+2213x^40+2200x^41+3388x^42+3212x^43+4245x^44+3516x^45+3794x^46+2408x^47+2147x^48+944x^49+874x^50+380x^51+276x^52+52x^53+66x^54+8x^55+15x^56+2x^58+1x^60

The gray image is a linear code over GF(2) with n=176, k=15 and d=72.
This code was found by Heurico 1.16 in 25 seconds.