The generator matrix

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

generates a code of length 46 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+49x^42+430x^43+802x^44+712x^45+620x^46+508x^47+298x^48+272x^49+222x^50+102x^51+49x^52+24x^53+4x^54+1x^56+1x^58+1x^60

The gray image is a code over GF(2) with n=368, k=12 and d=168.
This code was found by Heurico 1.16 in 0.125 seconds.