The generator matrix

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

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+211x^42+548x^43+374x^44+752x^45+408x^46+768x^47+353x^48+432x^49+138x^50+52x^51+38x^52+2x^54+8x^55+2x^56+7x^58+2x^62

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 6.72 seconds.