The generator matrix

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

generates a code of length 54 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+336x^47+1648x^48+3296x^49+6730x^50+10476x^51+14519x^52+18520x^53+19600x^54+19146x^55+15038x^56+10282x^57+6298x^58+2904x^59+1519x^60+484x^61+169x^62+76x^63+7x^64+10x^65+2x^66+4x^67+4x^68+1x^70+2x^71

The gray image is a code over GF(2) with n=432, k=17 and d=188.
This code was found by Heurico 1.16 in 111 seconds.