The generator matrix

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

generates a code of length 43 over Z2[X]/(X^4) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+2x^42+46x^43+2x^44+8x^45+1x^46+2x^47+1x^48+1x^54

The gray image is a linear code over GF(2) with n=344, k=6 and d=168.
This code was found by Heurico 1.16 in 0.047 seconds.