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

generates a code of length 45 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+495x^42+644x^43+882x^44+544x^45+626x^46+328x^47+228x^48+128x^49+157x^50+20x^51+40x^52+1x^56+2x^58

The gray image is a code over GF(2) with n=360, k=12 and d=168.
This code was found by Heurico 1.16 in 0.141 seconds.