The generator matrix

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

generates a code of length 43 over Z4[X]/(X^2+2X+2) 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 2.55 seconds.