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

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

Homogenous weight enumerator: w(x)=1x^0+76x^53+254x^54+500x^55+941x^56+1222x^57+2527x^58+3116x^59+5287x^60+6400x^61+8321x^62+8030x^63+8589x^64+6606x^65+5439x^66+3056x^67+2214x^68+1146x^69+887x^70+372x^71+243x^72+156x^73+66x^74+28x^75+31x^76+10x^77+10x^78+2x^79+6x^80

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 72.3 seconds.