The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+77x^54+8x^55+459x^56+56x^57+1317x^58+808x^59+3332x^60+3032x^61+5108x^62+4504x^63+5090x^64+2984x^65+3330x^66+824x^67+1253x^68+72x^69+347x^70+71x^72+47x^74+20x^76+12x^78+11x^80+2x^82+3x^84

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 13.7 seconds.