The generator matrix

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

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+332x^41+797x^42+1214x^43+1404x^44+1288x^45+1164x^46+740x^47+524x^48+444x^49+177x^50+62x^51+22x^52+16x^53+6x^54+1x^56

The gray image is a code over GF(2) with n=360, k=13 and d=164.
This code was found by Heurico 1.16 in 0.469 seconds.