The generator matrix

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

generates a code of length 45 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+238x^39+1470x^40+2912x^41+5381x^42+7674x^43+9491x^44+11098x^45+10003x^46+7472x^47+5347x^48+2670x^49+1200x^50+402x^51+103x^52+38x^53+23x^54+6x^55+4x^56+2x^57+1x^58

The gray image is a code over GF(2) with n=360, k=16 and d=156.
This code was found by Heurico 1.16 in 24.5 seconds.