The generator matrix

 1  0  1  1  1  2 X^2+X  1  1  1  1 X^2  1  1 X^2+X+2  1  1  X  1  1 X^2+2  1  1 X+2  1  1  2  1  1  0  1  1  1  1 X+2  1  1  1 X^2+2  X  1  1  1
 0  1 X+1 X^2+X+2 X^2+1  1  1  X X+1 X^2+X X^2+X+1  1  2 X^2+3  1 X^2  1  1 X^2+2 X^2+X+3  1 X+2  3  1  2 X+3  1 X^2 X^2+X  0  X  1 X^2+X+3 X^2+1  1 X+3 X+2 X^2+2  1  2  0  X  3
 0  0 X^2 X^2+2  2 X^2  0 X^2  2  0 X^2+2 X^2+2 X^2 X^2 X^2 X^2+2 X^2+2 X^2+2  0  2  0  0  2  0 X^2+2 X^2+2 X^2+2 X^2  2 X^2 X^2+2 X^2  0  0  2 X^2  2  2  2 X^2 X^2+2  0 X^2+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+256x^41+229x^42+232x^43+109x^44+60x^45+41x^46+80x^47+1x^48+12x^49+1x^50+1x^54+1x^60

The gray image is a code over GF(2) with n=344, k=10 and d=164.
This code was found by Heurico 1.16 in 2.53 seconds.