The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+130x^62+292x^63+472x^64+848x^65+711x^66+1288x^67+780x^68+1316x^69+691x^70+836x^71+377x^72+264x^73+111x^74+16x^75+25x^76+4x^77+11x^78+4x^80+10x^82+1x^84+2x^88+2x^92

The gray image is a code over GF(2) with n=544, k=13 and d=248.
This code was found by Heurico 1.16 in 1.23 seconds.