The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+326x^41+801x^42+1228x^43+1331x^44+1450x^45+1007x^46+830x^47+541x^48+324x^49+207x^50+118x^51+15x^52+12x^53+1x^54

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 0.453 seconds.