The generator matrix

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

generates a code of length 68 over Z16 who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+68x^62+624x^63+1145x^64+1816x^65+1558x^66+2434x^67+1847x^68+2174x^69+1454x^70+1340x^71+743x^72+586x^73+296x^74+182x^75+38x^76+30x^77+11x^78+28x^79+1x^80+2x^81+4x^82+1x^84+1x^86

The gray image is a code over GF(2) with n=544, k=14 and d=248.
This code was found by Heurico 1.16 in 2.71 seconds.