The generator matrix

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

generates a code of length 68 over Z16 who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+80x^61+438x^62+1316x^63+1908x^64+3020x^65+3337x^66+4432x^67+4227x^68+4552x^69+3177x^70+2524x^71+1687x^72+1088x^73+441x^74+284x^75+109x^76+88x^77+25x^78+16x^79+4x^80+4x^81+6x^82+4x^83

The gray image is a code over GF(2) with n=544, k=15 and d=244.
This code was found by Heurico 1.16 in 10.8 seconds.