The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+88x^62+652x^63+1162x^64+1516x^65+1980x^66+2040x^67+2139x^68+2038x^69+1611x^70+1226x^71+798x^72+514x^73+297x^74+164x^75+93x^76+26x^77+13x^78+14x^79+5x^80+2x^81+3x^82+2x^84

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 3.09 seconds.