The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+470x^42+790x^43+680x^44+676x^45+476x^46+392x^47+269x^48+172x^49+120x^50+18x^51+24x^52+4x^54+2x^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 10.7 seconds.