The generator matrix

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

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+232x^47+878x^48+1840x^49+2756x^50+3758x^51+4624x^52+5002x^53+4518x^54+3734x^55+2523x^56+1518x^57+772x^58+362x^59+138x^60+54x^61+42x^62+10x^63+4x^64+2x^65

The gray image is a code over GF(2) with n=424, k=15 and d=188.
This code was found by Heurico 1.16 in 8.36 seconds.