The generator matrix

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

generates a code of length 46 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+78x^43+47x^44+184x^45+416x^46+172x^47+46x^48+72x^49+6x^51+1x^52+1x^88

The gray image is a code over GF(2) with n=368, k=10 and d=172.
This code was found by Heurico 1.16 in 0.11 seconds.