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

generates a code of length 77 over Z16 who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+396x^71+118x^72+888x^73+400x^74+1184x^75+513x^76+1532x^77+524x^78+1040x^79+384x^80+580x^81+64x^82+284x^83+30x^84+144x^85+4x^86+68x^87+8x^88+20x^89+4x^91+1x^92+4x^93+1x^112

The gray image is a code over GF(2) with n=616, k=13 and d=284.
This code was found by Heurico 1.16 in 71.2 seconds.