The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+602x^47+1692x^48+3724x^49+5391x^50+7476x^51+9104x^52+9816x^53+8880x^54+7852x^55+5412x^56+3086x^57+1459x^58+736x^59+164x^60+92x^61+22x^62+18x^63+3x^64+2x^65+4x^67

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 28.9 seconds.