The generator matrix

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

generates a code of length 45 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+372x^41+660x^42+1458x^43+1094x^44+1536x^45+974x^46+960x^47+435x^48+400x^49+156x^50+110x^51+6x^52+28x^53+2x^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 0.422 seconds.