The generator matrix

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

generates a code of length 68 over Z16 who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+300x^63+535x^64+878x^65+986x^66+994x^67+1135x^68+886x^69+940x^70+688x^71+407x^72+238x^73+58x^74+52x^75+27x^76+34x^77+12x^79+4x^80+12x^81+2x^83+1x^84+1x^88+1x^92

The gray image is a code over GF(2) with n=544, k=13 and d=252.
This code was found by Heurico 1.16 in 94.8 seconds.