The generator matrix

 1  0  0  1  1  1  2  0 X^2 X^2  1  1  1  1 X^2+X+2  1 X^2+X  1  1 X^2+X+2  1  1 X^2+X+2  X X+2  1  1  1  1 X^2+2  1  0  1 X^2  1  1  1 X^2  1  1 X+2  0  1 X+2  1  1
 0  1  0  0 X^2+1 X^2+1  1 X^2+X  1  1 X^2+3  2 X^2  3 X+2 X+3  1 X^2+X+2 X+2  1 X+3 X^2+2  2  1  1  X  3  1 X+2  2 X^2+X  1  0  1 X^2+X+1 X^2+2  X  1  1 X^2+X+2  1 X+2 X+2 X^2 X+3 X^2
 0  0  1 X+1 X+3  2 X^2+X+3  1  X  1  1 X^2+X  3 X+2  1 X^2 X^2+X+2 X^2 X+2 X^2+X+1 X^2+X+1 X^2+1  1 X^2+X  1  1 X+1  0 X^2+3  1  0 X^2+2  2 X+1  3  X X+3 X^2+3 X^2+X X+2 X+2  1  0  1 X^2+X+2 X^2+X+1
 0  0  0  2  2  0  2  2  2  0  0  2  0  2  0  0  2  2  0  0  2  2  2  0  2  2  0  2  0  2  0  2  2  0  2  0  0  2  0  2  0  0  2  0  2  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+306x^42+824x^43+1323x^44+1226x^45+1458x^46+998x^47+839x^48+506x^49+366x^50+190x^51+107x^52+28x^53+14x^54+4x^55+2x^56

The gray image is a code over GF(2) with n=368, k=13 and d=168.
This code was found by Heurico 1.16 in 0.438 seconds.