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

generates a code of length 71 over Z16 who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+350x^62+572x^63+1089x^64+1580x^65+2598x^66+3242x^67+5016x^68+6572x^69+7249x^70+8956x^71+7596x^72+6628x^73+4967x^74+3160x^75+2414x^76+1336x^77+1047x^78+540x^79+342x^80+136x^81+74x^82+38x^83+22x^84+4x^85+2x^86+4x^87+1x^98

The gray image is a code over GF(2) with n=568, k=16 and d=248.
This code was found by Heurico 1.16 in 83.5 seconds.