The generator matrix

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

generates a code of length 77 over Z16 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+200x^68+296x^69+924x^70+1096x^71+2418x^72+3376x^73+5554x^74+6188x^75+8935x^76+7864x^77+8918x^78+6288x^79+5489x^80+3108x^81+2316x^82+1132x^83+663x^84+248x^85+238x^86+80x^87+104x^88+20x^89+54x^90+10x^92+12x^94+3x^96+1x^104

The gray image is a code over GF(2) with n=616, k=16 and d=272.
This code was found by Heurico 1.16 in 63.2 seconds.