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  X  X X^2  1  X  1  1  0  1  1  1  X  1  0  X  1  1 X^2
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2  0  X X^2+X  X X^2+X X^2+X  0 X^2+X X^2+X  0 X^2+X X^2  0  0 X^2+X X^2+X  X X^2 X^2+X X^2 X^2+X  X X^2+X X^2+X  X X^2 X^2  X X^2  0 X^2 X^2
 0  0  X  0  X  X X^2+X  0  0  0 X^2+X X^2+X  X  X X^2  0  X  0 X^2  0  0 X^2  X  X X^2 X^2 X^2 X^2+X X^2+X  X X^2+X X^2+X X^2+X  X  X X^2  X X^2  0  X X^2+X X^2+X  X
 0  0  0  X  X  0 X^2+X  X X^2 X^2+X  X X^2 X^2  X  X X^2  0 X^2 X^2+X  0 X^2+X X^2+X  X  X  0 X^2  0 X^2  0  X X^2 X^2  X X^2+X  X  0  0  X X^2  0 X^2  X  X
 0  0  0  0 X^2  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2
 0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0
 0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0  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+177x^36+308x^38+72x^39+471x^40+264x^41+614x^42+368x^43+635x^44+240x^45+390x^46+72x^47+257x^48+8x^49+146x^50+50x^52+14x^54+7x^56+1x^60+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 0.743 seconds.