The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+332x^63+549x^64+888x^65+977x^66+1090x^67+997x^68+982x^69+803x^70+622x^71+327x^72+324x^73+128x^74+58x^75+37x^76+42x^77+11x^78+10x^79+8x^80+4x^81+1x^82+1x^88

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 6.25 seconds.