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

generates a code of length 70 over Z16 who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+463x^62+132x^63+1404x^64+684x^65+2506x^66+1716x^67+3775x^68+3608x^69+4498x^70+3560x^71+3668x^72+1924x^73+2276x^74+500x^75+1174x^76+112x^77+519x^78+44x^79+142x^80+8x^81+34x^82+11x^84+8x^86+1x^96

The gray image is a code over GF(2) with n=560, k=15 and d=248.
This code was found by Heurico 1.16 in 37.3 seconds.