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

generates a code of length 43 over Z2[X]/(X^4) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+72x^38+200x^39+221x^40+608x^41+480x^42+944x^43+480x^44+608x^45+210x^46+200x^47+63x^48+4x^54+3x^56+2x^62

The gray image is a linear code over GF(2) with n=344, k=12 and d=152.
This code was found by Heurico 1.16 in 0.172 seconds.