The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  X X^2+X  1 X^2 X^2+X  1  1 X^2+X X^2+X  1  1  1 X^2+X  1 X^2+X  1  1  0 X^2  X  0  1  1  1  X  1  1  0  0  1 X^2  1  1
 0  1  0  0  0  1  1  1 X^2+X+1 X^2+1  X  1 X^2+X X^2  1 X^2 X^2+X  1  1  1 X^2+1  0 X^2  1 X+1 X^2+X X^2+X  X X^2+X  1  1  0 X^2 X^2+X X^2+X  1  1 X^2  1  1 X^2+X  0 X+1 X+1
 0  0  1  0  1  1  0  1 X^2+1 X^2+X  X X^2+1  1  1  0 X^2  1 X^2+X+1 X+1  0 X^2+1  X X^2+X+1 X+1 X^2  1 X^2+X+1 X^2+X  1  X X^2+1  1 X^2+X X+1 X^2+X X^2 X+1  X X^2+X X^2+X X^2+X+1  1  0 X+1
 0  0  0  1  1  0  1 X^2+1 X^2+X+1 X^2 X^2+X+1  0 X+1 X^2  1  1  1 X^2+1 X^2 X+1 X^2+X  X X^2+X X^2+X+1  0 X^2+1 X^2+X X^2+1  0 X^2 X^2+1 X+1 X^2+1  0 X^2+1  1 X^2+X X^2+X  0 X+1 X+1 X^2+X  0  0
 0  0  0  0 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2
 0  0  0  0  0 X^2  0  0  0  0  0  0  0 X^2  0  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0
 0  0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  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+221x^36+436x^37+1074x^38+1224x^39+2222x^40+2188x^41+3560x^42+3260x^43+4209x^44+3340x^45+3792x^46+2356x^47+2161x^48+1140x^49+868x^50+324x^51+247x^52+64x^53+46x^54+4x^55+24x^56+4x^58+3x^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 24.4 seconds.