The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+60x^62+320x^63+563x^64+1426x^65+2010x^66+3786x^67+4805x^68+7374x^69+8111x^70+9028x^71+7810x^72+7536x^73+4799x^74+3754x^75+1807x^76+1134x^77+535x^78+312x^79+169x^80+90x^81+33x^82+40x^83+8x^84+8x^85+2x^86+8x^87+5x^88+2x^90

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 53.6 seconds.