The generator matrix

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

generates a code of length 71 over Z16 who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+138x^65+261x^66+574x^67+556x^68+1228x^69+721x^70+1298x^71+715x^72+1206x^73+551x^74+538x^75+261x^76+104x^77+3x^78+12x^79+4x^81+4x^83+1x^84+8x^85+6x^87+1x^92+1x^108

The gray image is a code over GF(2) with n=568, k=13 and d=260.
This code was found by Heurico 1.16 in 6.72 seconds.