The generator matrix

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

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+214x^40+396x^41+315x^42+354x^43+259x^44+224x^45+163x^46+74x^47+21x^48+8x^49+17x^50+1x^56+1x^58

The gray image is a linear code over GF(2) with n=344, k=11 and d=160.
This code was found by Heurico 1.16 in 0.422 seconds.