The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+487x^62+1176x^63+2073x^64+3028x^65+3781x^66+4268x^67+4065x^68+3924x^69+3571x^70+2644x^71+1670x^72+1068x^73+547x^74+228x^75+122x^76+44x^77+44x^78+4x^79+4x^80+16x^82+1x^84+2x^86

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 60.4 seconds.