The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  4  1  1  2  2  4  1  8  1  2  1  1  2  8  8  1  1  0  1  1  1  2  1  1  1  2  2  2  2  1  4  1  1  2  2  4  8  1  1  2  2 12  1
 0  2  0  2  0  0 14 14  4  6  2  4 12 10 14  4 12  2  0  8  8 14  0 14  6 12  4  4  2  6  2 14  8  2 12  2 14 10  8 10 12  2  0  6  6  0 10  8  8  0 14 12 12  6 14 10 14  2 12  6 10  8  0  8  2  4 12  6  2  2  4
 0  0  2  2 12  6  6  4  4  0  6 10  8  4 10 10  2  2 14  0 12 10  2  8  4  6  0  2  8  4  2  4  6  2  0  0 14  2  0 12 14  8  2 14 12  2 12  6  4  6  8  6  8  2 12  8  4  0  2 12  4 14 14  2  8  8  6  2  6  8 12
 0  0  0  4  0  0  4  8  0  0 12  8  0  8 12  0  4  0  4 12 12  8  4 12  4  4  4  8  4  4  4  0  4  8 12  8  8  4  0  0 12 12  4  0  8  8 12  0 12  8  0 12  4  0  4  8 12  8  0 12  0  8  4  8  8  0  0 12 12  0  0
 0  0  0  0  8  0  0  0  0  8  8  8  8  8  8  8  0  8  8  0  8  0  0  0  8  8  0  0  8  0  8  0  0  0  8  8  8  8  0  8  8  8  8  0  8  0  8  8  8  8  0  8  0  0  0  8  0  0  0  0  8  0  0  0  8  0  8  8  0  0  8
 0  0  0  0  0  8  8  8  8  8  0  8  8  0  8  0  0  8  8  8  0  8  8  8  0  0  0  0  0  0  8  0  0  8  8  0  0  8  8  0  8  8  0  0  8  0  0  8  8  8  0  0  8  8  0  8  8  8  8  0  8  0  8  8  8  0  0  8  0  8  8

generates a code of length 71 over Z16 who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+70x^63+293x^64+438x^65+636x^66+1134x^67+1114x^68+1878x^69+1443x^70+2466x^71+1818x^72+1706x^73+1021x^74+894x^75+523x^76+398x^77+208x^78+158x^79+73x^80+48x^81+19x^82+10x^83+15x^84+12x^85+2x^87+3x^88+2x^91+1x^94

The gray image is a code over GF(2) with n=568, k=14 and d=252.
This code was found by Heurico 1.16 in 6.09 seconds.