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  1  1  1  1  X  0  1  X X^2  1  X  X  1  1 X^2  0  1  X  X  1  1
 0  X  0  0  0  0  0  0  0 X^2+X  X  X  X  0  X X^2+X X^2  X  X X^2+X  0 X^2 X^2+X X^2 X^2+X  X X^2 X^2+X  X  0 X^2  0 X^2+X X^2  0  X X^2  X  X X^2+X X^2+X X^2+X X^2  0
 0  0  X  0  0  0  X X^2+X  X X^2  X X^2+X  0 X^2+X  0 X^2+X X^2+X X^2  0  X X^2 X^2+X  X  0  X  X  X  X  0 X^2  X  X  0  X  X  0 X^2  X X^2  X  0  X  X X^2
 0  0  0  X  0  X  X  X  0 X^2+X X^2  X X^2+X  X X^2+X X^2 X^2  0 X^2  0  0  X X^2+X  0 X^2  0 X^2+X X^2+X  0 X^2+X  X X^2+X X^2  X  0 X^2 X^2+X X^2+X X^2+X X^2+X  0 X^2+X  0  0
 0  0  0  0  X  X  0  X X^2+X  X  0  X X^2 X^2+X X^2  0 X^2+X X^2  X  X X^2+X X^2 X^2 X^2 X^2+X  0  X  0  0 X^2+X  X  0  X  X  X  X X^2 X^2+X X^2+X  0  0 X^2+X  X X^2+X
 0  0  0  0  0 X^2  0  0  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2
 0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0  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+244x^36+456x^38+56x^39+701x^40+280x^41+1052x^42+688x^43+1268x^44+688x^45+1084x^46+280x^47+705x^48+56x^49+344x^50+191x^52+68x^54+25x^56+4x^58+1x^68

The gray image is a linear code over GF(2) with n=176, k=13 and d=72.
This code was found by Heurico 1.16 in 42.1 seconds.