The generator matrix

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

generates a code of length 52 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+166x^45+1656x^46+3250x^47+6688x^48+9858x^49+14651x^50+18078x^51+21964x^52+18084x^53+16087x^54+9656x^55+5978x^56+2896x^57+1379x^58+400x^59+184x^60+62x^61+17x^62+6x^63+1x^64+6x^65+2x^66+2x^67

The gray image is a code over GF(2) with n=416, k=17 and d=180.
This code was found by Heurico 1.16 in 104 seconds.