The generator matrix

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

generates a code of length 63 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+791x^56+2012x^57+4602x^58+7020x^59+10879x^60+13704x^61+17280x^62+18044x^63+17853x^64+14064x^65+11284x^66+6620x^67+3955x^68+1660x^69+778x^70+340x^71+114x^72+12x^73+30x^74+8x^75+6x^76+4x^77+10x^78+1x^80

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 355 seconds.