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

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

Homogenous weight enumerator: w(x)=1x^0+57x^62+306x^63+621x^64+884x^65+1233x^66+1618x^67+2519x^68+3278x^69+4075x^70+3846x^71+4199x^72+3230x^73+2311x^74+1596x^75+1163x^76+680x^77+458x^78+284x^79+181x^80+114x^81+51x^82+30x^83+18x^84+6x^85+6x^86+2x^88+1x^98

The gray image is a code over GF(2) with n=568, k=15 and d=248.
This code was found by Heurico 1.16 in 20.6 seconds.