The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  X  0  1  1  1  1  X  X  0  0  1  1  1  1  1  1  X  1  0  X  1  X
 0  X  0 X^2+X  0 X^2+X  0 X^2+X  0 X^2+X X^2  0 X^2+X X^2+X  X  0 X^2  0 X^2  0 X^2+X  X X^2+X  X X^2+X  X X^2+X X^2+X X^2+X X^2+X  X  X  0 X^2 X^2+X X^2  X X^2+X X^2+X  0  X  0  X X^2
 0  0 X^2  0  0  0  0  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2  0
 0  0  0 X^2  0  0  0  0  0  0  0  0 X^2 X^2 X^2  0  0  0  0  0  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2
 0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0
 0  0  0  0  0 X^2  0  0  0 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0
 0  0  0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2
 0  0  0  0  0  0  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0
 0  0  0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 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+153x^36+136x^38+64x^39+313x^40+320x^41+248x^42+640x^43+386x^44+640x^45+248x^46+320x^47+276x^48+64x^49+136x^50+109x^52+33x^56+8x^60+1x^64

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 0.926 seconds.