The generator matrix

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

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+30x^40+408x^41+30x^42+96x^43+32x^44+384x^45+32x^46+1x^48+8x^49+1x^50+1x^66

The gray image is a linear code over GF(2) with n=344, k=10 and d=160.
This code was found by Heurico 1.16 in 0.046 seconds.