The generator matrix

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

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+30x^36+108x^37+221x^38+276x^39+312x^40+430x^41+452x^42+468x^43+520x^44+416x^45+291x^46+228x^47+141x^48+70x^49+54x^50+36x^51+15x^52+16x^53+6x^54+4x^56+1x^60

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 0.506 seconds.