The generator matrix

 1  0  1  1  1  6  8  1  1  1  1  6  8  1  1 14  1  1  1 10  1  1  1  8 14  1  1 12  1  1 10  1  4  1  8  1  4  1  1  1  1  2  1  1  6  1  1  4 14  1  1  1  1  1  2  0  1  1  1  1  1  1  1 14  0  1  2 12  1 14  1
 0  1 11  6  1  1  1  0  3  2  9  1  1  8  3  1 14  5  3  1 12 13  0  1  1  6  5  1  7  8  1 14  1  8  1 15  1  5  6 11  6  1  1  2  1  2  5  1  1  0 11  4  2 11  1  1  3 10  3  8  6  5  2  1  1  5  4  1  9  1  0
 0  0 12  0  0  0  0  4  8  4  4  4  4  8 12  8 12  0  0  8  0 12  4 12  8 12  8  4  0  4  4 12  4  0 12  4  0  4  0  0 12 12 12  8  8  8  4  8  4  0  0  4  0  8  8 12 12  0 12 12  0  4  8  0 12  0  0  8  8  0  8
 0  0  0 12  0  0  0  0  4 12  4 12  8  0  8  4  0  8  4  4  4  4  4 12  8  4  4  4  8  8 12 12  0 12  8  0 12  4  0  8  0 12  0  4 12  0  8  4  8 12 12  0  0 12  0  4 12  4 12  8  4 12  8 12  0 12  4  0  4  4  8
 0  0  0  0  4  0 12  4  4  4  0  0  8 12  4  0  8  0  8 12 12 12  8  4  4  8 12  0  4  0 12 12  8 12 12 12 12  8  0  4  4  4  0  0  8  4 12  8  0  8  8  0  4  0  0  8 12  0  4  8  8  0  0  8 12  0 12  8 12  0  0
 0  0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  0  8  8  8  8  8  8  8  8  0  8  8  8  8  8  8  0  8  0  0  8  8  8  8  0  0  0  0  8  0  8  0  8  8  0  0  8  8  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+42x^62+152x^63+186x^64+708x^65+816x^66+1934x^67+2093x^68+4270x^69+3535x^70+5408x^71+3595x^72+4290x^73+2062x^74+1902x^75+687x^76+592x^77+200x^78+106x^79+47x^80+36x^81+30x^82+28x^83+10x^84+18x^85+3x^86+6x^87+2x^88+6x^89+2x^92+1x^96

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 16 seconds.