The generator matrix

 1  0  1  1  1 X^3+X^2+X  1  1 X^3+X^2  1  1 X^3  1  1  X  1  1  1  1  X  1  1 X^2 X^2+X X^3+X^2 X^3+X X^3 X^2+X  X X^3 X^3+X^2+X X^3 X^3+X^2+X  0  1  1  1  1  1  1  0 X^3+X^2 X^3+X
 0  1 X+1 X^3+X^2+X X^2+1  1 X^3 X^2+X+1  1 X^3+X^2 X+1  1  X X^3+1  1 X^2 X^3+X^2+1 X^2+X X^3+X^2+X+1  1 X^3+X  1  1  1  1  1  1  1  1  1  1  1  1  1 X^3 X^3+X^2+X+1  1 X^3+X^2 X^2+1 X^3+X^2+X+1  0  1  1
 0  0 X^2 X^2 X^3 X^2 X^3+X^2 X^3+X^2 X^3 X^3  0 X^3+X^2 X^2 X^3 X^2 X^3+X^2 X^2  0  0 X^2 X^3 X^3+X^2 X^3+X^2  0  0 X^3 X^2 X^3  0 X^3 X^3+X^2 X^3+X^2 X^3 X^2 X^2 X^3 X^3+X^2 X^3  0  0 X^2  0 X^3
 0  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0  0  0 X^3  0 X^3  0  0 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0 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+308x^40+304x^41+244x^42+336x^43+355x^44+208x^45+204x^46+48x^47+34x^48+4x^52+1x^60+1x^64

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 19 seconds.