The generator matrix

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

generates a code of length 45 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+168x^41+427x^42+560x^43+702x^44+618x^45+585x^46+454x^47+305x^48+132x^49+70x^50+32x^51+16x^52+18x^53+4x^54+2x^55+1x^58+1x^62

The gray image is a code over GF(2) with n=360, k=12 and d=164.
This code was found by Heurico 1.16 in 0.188 seconds.