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

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+230x^36+468x^38+16x^39+705x^40+280x^41+996x^42+704x^43+1336x^44+784x^45+1086x^46+240x^47+681x^48+24x^49+382x^50+170x^52+70x^54+12x^56+6x^58+1x^72

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 26.8 seconds.