The generator matrix

 1  0  1  1 X^2  1  1  1 X^2+X  1  1  X  1  1  0  1  1  X  1  1  1  1  1 X^2+2  1 X^2+X+2  1  1  1  1  1  1  1 X^2+2 X^2+X+2  1  1 X^2 X^2+X+2 X^2  1  1  0  1 X^2+X+2  1
 0  1  1 X^2+X  1 X^2+X+1 X^2  3  1 X+2 X+1  1 X^2 X+1  1 X^2+X+3  2  1  0 X^2+1  2  2  2  1 X^2+3  1 X+2 X+2 X^2+X  X  X X+2 X^2+X+3  1  1  3 X+1  1  1 X^2 X^2+3  3  1 X^2+1  1 X^2+2
 0  0  X  0 X+2  X X+2  2  0 X^2+X+2  2 X+2 X^2+X+2 X^2+X X^2+2 X^2+2 X^2 X^2+X+2 X^2+X X^2+X+2 X^2+2 X+2  0 X^2+X+2 X^2 X^2+2 X^2+X+2  2 X^2 X^2  X X+2 X^2+X  2  X  0 X^2 X+2  0 X^2 X^2+X  X X^2+X+2 X+2 X^2  0
 0  0  0  2  0  2  2  2  2  0  0  2  2  2  0  0  0  2  0  0  2  0  2  0  2  2  2  0  2  0  0  2  0  2  0  0  2  2  0  0  2  2  2  2  0  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+75x^42+540x^43+748x^44+576x^45+454x^46+524x^47+606x^48+264x^49+165x^50+64x^51+52x^52+16x^53+8x^54+1x^56+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 0.187 seconds.