The generator matrix

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

generates a code of length 63 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+396x^57+1079x^58+2052x^59+2895x^60+4094x^61+3968x^62+4374x^63+4152x^64+3686x^65+2517x^66+1776x^67+849x^68+486x^69+214x^70+114x^71+47x^72+42x^73+22x^74+4x^75

The gray image is a code over GF(2) with n=504, k=15 and d=228.
This code was found by Heurico 1.16 in 10.3 seconds.