The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+342x^62+1212x^63+2536x^64+3046x^65+3391x^66+4074x^67+4262x^68+4094x^69+3391x^70+2444x^71+1888x^72+1054x^73+509x^74+232x^75+151x^76+78x^77+23x^78+20x^79+17x^80+2x^83+1x^84

The gray image is a code over GF(2) with n=544, k=15 and d=248.
This code was found by Heurico 1.16 in 10.8 seconds.