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

generates a code of length 43 over Z2[X]/(X^3) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+173x^36+4x^37+328x^38+76x^39+435x^40+240x^41+636x^42+376x^43+645x^44+260x^45+382x^46+60x^47+246x^48+8x^49+144x^50+61x^52+14x^54+6x^56+1x^68

The gray image is a linear code over GF(2) with n=172, k=12 and d=72.
This code was found by Heurico 1.16 in 0.783 seconds.