The generator matrix

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

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+43x^36+130x^37+193x^38+268x^39+331x^40+436x^41+454x^42+432x^43+497x^44+392x^45+327x^46+282x^47+128x^48+54x^49+45x^50+36x^51+14x^52+10x^53+4x^54+6x^55+8x^56+2x^57+1x^58+2x^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 0.517 seconds.