The generator matrix

 1  0  1  1 X^2  1  1  1 X^2+X  1  1  X  1  1  0  1  1  X  1  1  1 X^2+X+2 X^2+X+2  1  1  1 X^2+2  1  1 X^2+2  1 X^2+2 X^2+X+2  1  1  1  1  1  1 X^2  1  1 X^2 X^2+X+2  1
 0  1  1 X^2+X  1 X^2+X+1 X^2  3  1 X+2 X+1  1 X^2 X+1  1 X^2+X+3  2  1  0 X^2+1  2  1  1  2  2 X+2  1 X+2  X  1 X^2+X  1  1  3 X^2+X+1  3 X^2+1 X^2+X+1 X^2+3 X^2+2 X+3 X^2+X+1  1  1 X^2+2
 0  0  X  0 X+2  X X+2  2  0 X^2+X+2  2 X+2 X^2+X+2 X^2+X X^2+2 X^2+2 X^2 X^2+X+2 X^2+X X^2+X+2 X^2+2  X X^2+2 X+2  0 X^2+X+2 X^2+X+2 X^2+2  2 X^2 X^2+2 X^2+X X^2+2 X^2+X+2 X^2  2  X X^2+X+2 X^2 X^2+2 X+2 X^2+2  0  2 X^2+X
 0  0  0  2  0  2  2  2  2  0  0  2  2  2  0  0  0  2  0  0  2  0  2  0  2  2  0  0  0  2  2  2  0  2  2  0  2  0  2  0  0  2  2  0  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+128x^41+414x^42+820x^43+561x^44+500x^45+440x^46+676x^47+275x^48+140x^49+72x^50+40x^51+26x^52+2x^58+1x^60

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 0.172 seconds.