The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  8  4  2  2  0  1  0  1  1  4  2  1  1  0  8 12  2  2 12  1  1  1 12  1  2 12  1  1  1  1 12  2  2  1  1  1  2  1
 0  2  0  2  0  0  2 10  8  0  6  6  4  2 12  2 12 14 12  6  0  8  2 10  6  0  2  4 10  8  2  2 14  0  2  2  2 14  8  2 12  6  2 12 14 12 10  2 14  2  0  2 10  0  0  2 10 14 14  0 10 14  8
 0  0  2  2  0  6 10  8  6  4  6 12 12 12  2 14 12 14  2  4 12 10 14 12  4  2  4  2  2  2  6 14  0  2  0 12 10 12  2  6  2  2 12  2  2  6  2  8 14  8  2  4 10 12  4  2  4  8  4  2 14 12  0
 0  0  0  4  0  0  4  0  0  0 12  0  0  0  8  4  0  4  8  8  8  8 12  8  4 12 12 12 12 12  0  8 12  4  8  0  8 12  0  8  4  4 12  8  0 12  0  4  4  8  4  4  8 12  4  0  4  0 12  4  8  4  0
 0  0  0  0 12  0 12  4  4  4 12  4  8  0 12  8 12  8  8  0  8  4 12 12  8  0  4 12  0  4  4  8  8  8 12  8  8 12  8  4  0  0  4  0  0  4  4  0  0  4  4 12  0  4 12  8  4  8  4  8 12  4  4
 0  0  0  0  0  8  0  0  8  8  8  8  8  8  0  8  0  0  8  0  8  0  8  8  0  0  0  8  8  0  0  8  0  0  8  0  0  0  0  0  8  8  8  8  8  8  8  8  8  0  0  8  0  0  8  0  8  8  0  8  0  8  0

generates a code of length 63 over Z16 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+47x^54+250x^55+404x^56+804x^57+1172x^58+1836x^59+2467x^60+3158x^61+4077x^62+4364x^63+4247x^64+3268x^65+2413x^66+1642x^67+1088x^68+728x^69+323x^70+232x^71+96x^72+56x^73+26x^74+26x^75+17x^76+18x^77+5x^78+2x^79+1x^82

The gray image is a code over GF(2) with n=504, k=15 and d=216.
This code was found by Heurico 1.16 in 19.1 seconds.