The generator matrix

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

generates a code of length 63 over Z16 who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+48x^53+150x^54+298x^55+482x^56+950x^57+1789x^58+3318x^59+5149x^60+6984x^61+8912x^62+9422x^63+8806x^64+7402x^65+5094x^66+3098x^67+1714x^68+908x^69+446x^70+204x^71+140x^72+78x^73+45x^74+40x^75+25x^76+12x^77+12x^78+4x^79+3x^80+2x^81

The gray image is a code over GF(2) with n=504, k=16 and d=212.
This code was found by Heurico 1.16 in 51.2 seconds.