The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+116x^61+232x^62+550x^63+957x^64+1462x^65+1814x^66+1968x^67+2263x^68+2116x^69+1814x^70+1334x^71+865x^72+490x^73+152x^74+88x^75+60x^76+32x^77+14x^78+24x^79+7x^80+4x^81+6x^82+4x^83+4x^84+4x^85+2x^88+1x^92

The gray image is a code over GF(2) with n=544, k=14 and d=244.
This code was found by Heurico 1.16 in 45.2 seconds.