The generator matrix

 1  0  1  1  6  1  1  1  4  1  1  4  2  1  1  1 14  1  1  1 10  8  1  1 10  1  1  1  1 12 14  1  1  8  1  1  1  1 14  4  1  1  1  1 14  1  1  6  0  1  4  1  1  1  1  1  1  8  8  4 12  0  1
 0  1  1  6  1  3  5  4  1  7  2  1  1  8 15 15  1 10  9 14  1  1  9 10  1 12  5 14  3  1  1  2  7  1  3  4 13 14  1  1 13 10  8 11  1  3  0  1  0  0  1 11  9 15  0  3 13  1  1  1  1  2  0
 0  0  2  0  0  0  0  2  2  2 10  4  2  4  6  8  4  8 14  2 14  2  8 14  0  6  6  4  8  6  2 12  4 12 14 10 12 12 12  2  2 14 14  2 10  2  6  6  2  0  0  4  0  4  0  8 14  4  8 10  0  6  0
 0  0  0  8  0  0  0  0  0  0  0  0  8  0  8  8  8  8  0  8  8  0  0  0  0  8  0  0  0  8  8  8  0  8  8  8  8  8  0  0  8  0  0  8  0  8  0  8  0  8  8  0  8  0  8  8  8  0  8  8  0  8  8
 0  0  0  0  8  0  0  8  8  8  0  0  0  8  8  0  0  8  8  8  0  8  0  8  8  0  0  0  8  8  0  8  8  8  8  8  8  8  0  8  0  0  0  0  8  8  0  8  0  0  8  0  0  0  0  8  0  0  0  8  8  0  8
 0  0  0  0  0  8  0  0  0  0  0  0  0  0  0  8  8  0  8  8  8  8  8  8  0  0  8  0  0  8  0  0  8  8  8  0  0  8  8  0  8  8  0  0  8  8  8  0  0  8  0  0  0  8  8  0  8  8  8  8  8  8  8
 0  0  0  0  0  0  8  0  8  8  8  8  0  8  8  0  0  8  8  0  0  8  8  0  8  0  8  8  8  0  8  0  8  0  0  0  8  0  0  0  0  8  0  0  0  8  0  0  8  0  8  0  8  8  8  0  8  8  0  8  0  0  0

generates a code of length 63 over Z16 who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+56x^55+226x^56+570x^57+850x^58+1732x^59+2385x^60+3696x^61+4637x^62+4934x^63+4222x^64+3668x^65+2539x^66+1594x^67+770x^68+464x^69+141x^70+114x^71+71x^72+38x^73+23x^74+18x^75+8x^77+2x^78+4x^80+4x^81+1x^84

The gray image is a code over GF(2) with n=504, k=15 and d=220.
This code was found by Heurico 1.16 in 12.7 seconds.