The generator matrix

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

generates a code of length 71 over Z16 who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+58x^63+295x^64+780x^65+1112x^66+1844x^67+2553x^68+3632x^69+4140x^70+4422x^71+3871x^72+3612x^73+2523x^74+1724x^75+970x^76+588x^77+302x^78+158x^79+71x^80+56x^81+14x^82+8x^83+12x^84+4x^85+2x^86+10x^87+2x^88+3x^90+1x^92

The gray image is a code over GF(2) with n=568, k=15 and d=252.
This code was found by Heurico 1.16 in 14.8 seconds.