The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  1  X  X  X  1  X  1  X  1  1  1  1 X^2 X^2  X  1  1  X X^2
 0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  0  2  2  2  2  2  2  0  2  2  2  0  2  2  2  2  2  2  2  2  0  0  2  2  0
 0  0  2  0  0  0  0  0  0  0  2  2  2  2  2  0  2  2  2  2  2  0  2  2  2  0  2  2  0  0  2  2  2  0  0  2  0  0  0  0  2  2  0  0  0
 0  0  0  2  0  0  0  2  2  2  2  2  0  2  2  0  0  0  0  0  0  0  0  0  0  0  2  2  2  0  2  2  2  2  2  2  2  2  0  0  2  0  2  0  2
 0  0  0  0  2  0  2  2  2  0  0  0  0  2  2  0  0  0  2  2  2  2  0  2  2  2  2  0  0  2  0  2  0  2  2  2  0  0  0  0  0  2  2  0  0
 0  0  0  0  0  2  2  0  2  2  0  2  2  2  0  2  0  2  2  0  0  0  2  2  0  0  0  2  2  2  2  0  0  0  2  2  2  0  2  0  0  2  0  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+20x^41+33x^42+65x^44+284x^45+58x^46+26x^48+12x^49+3x^50+3x^52+4x^53+1x^54+1x^56+1x^62

The gray image is a code over GF(2) with n=360, k=9 and d=164.
This code was found by Heurico 1.16 in 6.03 seconds.