The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+265x^78+556x^79+2072x^80+2804x^81+4001x^82+5056x^83+6820x^84+7600x^85+7943x^86+7304x^87+6611x^88+5348x^89+3819x^90+2308x^91+1562x^92+600x^93+464x^94+132x^95+145x^96+32x^97+42x^98+4x^99+22x^100+8x^102+15x^104+2x^106

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 63.3 seconds.