The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+137x^62+216x^63+762x^64+1156x^65+2314x^66+2992x^67+5801x^68+6360x^69+9051x^70+8180x^71+8993x^72+6564x^73+5667x^74+2912x^75+2146x^76+1040x^77+598x^78+220x^79+254x^80+48x^81+71x^82+8x^83+14x^84+18x^86+10x^88+3x^92

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 56.6 seconds.