The generator matrix

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

generates a code of length 68 over Z16 who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+48x^61+309x^62+486x^63+1152x^64+1100x^65+2131x^66+1740x^67+2893x^68+1506x^69+2177x^70+954x^71+918x^72+364x^73+289x^74+148x^75+78x^76+18x^77+22x^78+28x^79+12x^80+4x^81+4x^83+1x^88+1x^92

The gray image is a code over GF(2) with n=544, k=14 and d=244.
This code was found by Heurico 1.16 in 3.61 seconds.