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

generates a code of length 77 over Z16 who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+58x^69+241x^70+502x^71+817x^72+980x^73+1374x^74+1552x^75+1935x^76+1950x^77+1852x^78+1460x^79+1222x^80+836x^81+586x^82+364x^83+255x^84+166x^85+109x^86+54x^87+36x^88+8x^89+12x^90+4x^91+5x^92+2x^93+2x^94+1x^108

The gray image is a code over GF(2) with n=616, k=14 and d=276.
This code was found by Heurico 1.16 in 6.21 seconds.