The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+424x^49+819x^50+1376x^51+1219x^52+1260x^53+976x^54+828x^55+443x^56+408x^57+187x^58+160x^59+62x^60+20x^61+2x^62+4x^63+2x^64+1x^68

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 0.735 seconds.