The generator matrix

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

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+502x^43+725x^44+738x^45+634x^46+490x^47+433x^48+274x^49+76x^50+136x^51+48x^52+36x^53+2x^58+1x^60

The gray image is a code over GF(2) with n=368, k=12 and d=172.
This code was found by Heurico 1.16 in 67.7 seconds.