The generator matrix

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

generates a code of length 63 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+176x^56+1162x^57+2442x^58+3598x^59+5757x^60+6754x^61+8599x^62+9022x^63+8599x^64+6572x^65+5527x^66+3688x^67+2009x^68+864x^69+437x^70+170x^71+102x^72+38x^73+11x^74+2x^75+4x^76+2x^77

The gray image is a code over GF(2) with n=504, k=16 and d=224.
This code was found by Heurico 1.16 in 33.2 seconds.