The generator matrix

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

generates a code of length 53 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+536x^47+1952x^48+3344x^49+5530x^50+7494x^51+9191x^52+9636x^53+9384x^54+7534x^55+5273x^56+2984x^57+1666x^58+642x^59+249x^60+68x^61+28x^62+18x^63+6x^64

The gray image is a code over GF(2) with n=424, k=16 and d=188.
This code was found by Heurico 1.16 in 30.1 seconds.