The generator matrix

 1  0  0  0  1  1  1 X+2  1  1 X+2 2X 2X+2  1  1 3X+2 2X+2 3X+2  0  1  1  1  1  1 3X+2 2X+2  1 2X  1  1  1  1  1 2X  1  1  1 3X+2  X  1  1  0  1  2  1  1  0 3X  2 3X+2 X+2 2X  1  1  2  1  1  X  1  1  1 X+2 3X
 0  1  0  0  0  3 3X+1  1 2X+2 2X+2  1  1 2X 2X+1 2X+3  0  1  1 X+2 3X 3X+3 3X+2 X+2  1  1  1 X+3 3X+2 X+1  2 3X+2  3 2X  1 2X+2 3X+3  X  2  1 2X+3  2  0 3X+3 X+2 X+1 3X  1  1  1  1 3X+2  1 X+1 2X+3  1 X+2  X 2X+2 2X+1  2 X+1  X  1
 0  0  1  0 2X+2 2X  2  0 2X+1 X+1 3X+1 3X+3  1 2X+1  3 X+2  3  0  1 3X+2 3X+2 2X  1 2X+3 3X+2 2X+3  1  1 3X+2  2  3 3X+1 3X X+1 X+2  3 X+3  2  2 3X  3  1 2X  X 3X+1  3 X+1 2X+2 3X 3X  1 3X 3X+3 3X+1 2X+3 3X+1 2X+2  1 X+2 3X+1  1  1  0
 0  0  0  1 3X+3 X+3 2X 3X+3 3X+3  0 X+1  2 X+3 3X+1 3X+2  1 X+1 2X+3 3X+1 3X+3 3X+1 2X X+1 2X+2 2X  X  3 3X+2 2X+2 3X 2X+1 2X+3 X+3 X+1 3X+2 2X X+1  1 X+1  3  2  X 3X+2  1 X+3 X+1 X+2 2X+2 2X X+2  X 3X  2 3X+2 3X+3 3X 2X+3  1 3X+2  X  X 2X+3 2X+3
 0  0  0  0 2X  0 2X 2X  0 2X  0 2X 2X 2X  0  0  0 2X 2X 2X  0  0  0  0  0 2X 2X  0 2X  0  0  0 2X 2X 2X 2X 2X 2X  0 2X 2X  0  0  0  0 2X  0 2X  0 2X 2X 2X  0 2X 2X  0  0 2X  0 2X  0 2X  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+702x^56+2176x^57+4265x^58+7320x^59+10695x^60+14520x^61+16658x^62+18008x^63+17404x^64+14868x^65+10601x^66+7068x^67+3739x^68+1728x^69+798x^70+304x^71+121x^72+52x^73+29x^74+4x^75+10x^76+1x^82

The gray image is a code over GF(2) with n=504, k=17 and d=224.
This code was found by Heurico 1.16 in 133 seconds.