The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2+2  1  1 X+2  1  1  0  1  1 X^2+X  1  1 X^2+2  1  1 X+2  1  1  0  1  1 X^2+X  1 X^2+2  1  1 X+2  1  X  1  1  1  X  1  1  X  1
 0  1 X+1 X^2+X X^2+1  1 X^2+X+3 X^2+2  1 X+2  3  1  0 X+1  1 X^2+X X^2+1  1 X^2+2 X^2+X+3  1 X+2  3  1  0 X+1  1 X^2+X+3 X^2+X  1 X^2+2  1 X^2+1 X+2  1 X^2+1 X^2+X X^2+3 X^2+X+3 X+3  X X^2+1  3 X+2 X^2+X+3
 0  0  2  0  0  0  0  2  2  2  2  2  0  0  0  0  0  0  2  2  2  2  2  2  0  0  0  2  2  2  0  0  2  2  2  0  0  2  0  2  0  0  0  2  0
 0  0  0  2  0  2  2  2  2  0  2  0  2  0  2  0  2  0  0  2  0  2  0  2  0  0  2  0  0  2  2  0  2  2  0  2  2  0  2  2  0  0  0  2  0
 0  0  0  0  2  0  2  2  2  2  0  2  0  2  0  0  2  0  2  0  2  2  0  2  2  0  2  2  0  0  2  2  2  0  0  0  0  2  0  0  2  0  2  0  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+84x^41+213x^42+164x^43+508x^44+172x^45+472x^46+136x^47+191x^48+60x^49+18x^50+20x^51+2x^52+4x^53+1x^58+2x^60

The gray image is a code over GF(2) with n=360, k=11 and d=164.
This code was found by Heurico 1.16 in 0.078 seconds.