The generator matrix

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

generates a code of length 86 over Z16 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+222x^78+980x^79+1694x^80+3012x^81+3922x^82+5252x^83+6682x^84+7306x^85+7809x^86+7468x^87+6561x^88+5352x^89+3686x^90+2514x^91+1403x^92+802x^93+368x^94+244x^95+108x^96+72x^97+28x^98+22x^99+13x^100+13x^102+2x^108

The gray image is a code over GF(2) with n=688, k=16 and d=312.
This code was found by Heurico 1.16 in 55.2 seconds.