The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+270x^62+352x^63+1339x^64+1284x^65+1992x^66+2000x^67+2233x^68+1948x^69+1897x^70+1224x^71+1107x^72+304x^73+235x^74+32x^75+63x^76+12x^77+49x^78+8x^79+22x^80+4x^81+5x^82+2x^88+1x^96

The gray image is a code over GF(2) with n=544, k=14 and d=248.
This code was found by Heurico 1.16 in 21.8 seconds.