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  1 X^3+X^2+X  1 X^2+X X^3+X^2+X  1  X  1
 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^2+1  X X^3+X^2+1  1  1  0  X X^3+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 X^3+X^2+X  1 X^2+1 X+1 X^3+X^2+1 X^3+X X^3+X^2 X^3+X+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+525x^40+626x^41+800x^42+606x^43+642x^44+258x^45+346x^46+122x^47+83x^48+52x^49+30x^50+4x^52+1x^56

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 0.484 seconds.