The generator matrix

 1  0  0  1  1  1 X^3  1  1  1  1 X^2  0 X^3+X^2+X  1  1 X^3+X  1  1  X  X  0 X^3+X^2+X X^2+X X^2  1  1 X^3+X  1  1 X^3  1  1 X^3+X^2  1 X^3+X^2  1  1  1  1  1 X^2+X  0
 0  1  0 X^3 X^2+1 X^3+X^2+1  1  X X^3+X X^3+X^2+X+1 X^2+X+1  1  1 X^2+X  1 X^3+X  1 X+1 X^2  0  1 X^2+X  1  1  1 X^3+X+1  X  1 X+1 X^2 X^3+X^2 X^3  1  1 X^2+X+1 X^3+X  X  0 X^3+1 X+1 X^2  1 X^2
 0  0  1 X^3+X+1 X+1 X^3 X^3+X+1 X^3+X X^3+1  1  X  1 X^3+X  1 X^3+X^2+1 X^2+X+1 X^2 X^3 X^2+X  1 X^2+X+1  1 X^3+X^2+X X^3+X^2+X+1 X^2+X+1 X^3+X+1 X^3+X^2+1 X^2+1 X^2 X^3+1  1 X^3+X^2+1  1 X^2+1 X^2+X  1 X^3+X^2 X^3+X^2  X X^3+X X^2+X+1 X^3  1

generates a code of length 43 over Z2[X]/(X^4) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+442x^40+624x^41+1036x^42+528x^43+539x^44+288x^45+296x^46+144x^47+155x^48+16x^49+20x^50+7x^52

The gray image is a linear code over GF(2) with n=344, k=12 and d=160.
This code was found by Heurico 1.16 in 0.875 seconds.