The generator matrix

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

generates a code of length 53 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+394x^49+795x^50+1544x^51+1105x^52+1334x^53+790x^54+928x^55+452x^56+428x^57+184x^58+146x^59+57x^60+20x^61+6x^62+6x^63+1x^64+1x^66

The gray image is a code over GF(2) with n=424, k=13 and d=196.
This code was found by Heurico 1.16 in 0.579 seconds.