The generator matrix

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

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+174x^41+405x^42+604x^43+627x^44+546x^45+687x^46+552x^47+264x^48+138x^49+39x^50+26x^51+19x^52+2x^53+2x^54+4x^57+2x^58+2x^59+1x^62+1x^64

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 97.7 seconds.