The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+154x^56+1088x^57+2406x^58+4000x^59+5437x^60+7176x^61+8224x^62+8756x^63+8407x^64+7352x^65+5298x^66+3572x^67+1977x^68+960x^69+424x^70+200x^71+44x^72+30x^73+4x^74+16x^75+4x^76+4x^78+2x^81

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 34.6 seconds.