The generator matrix

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

generates a code of length 43 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+76x^41+156x^42+112x^43+60x^44+64x^45+36x^46+2x^48+4x^49+1x^64

The gray image is a code over GF(2) with n=344, k=9 and d=164.
This code was found by Heurico 1.16 in 0.063 seconds.