The generator matrix

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

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+650x^56+2132x^57+4457x^58+7218x^59+10793x^60+13958x^61+17616x^62+17424x^63+17922x^64+14298x^65+10815x^66+6732x^67+3793x^68+1972x^69+882x^70+236x^71+113x^72+22x^73+19x^74+4x^75+6x^76+2x^77+2x^78+2x^80+1x^82+2x^83

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 129 seconds.