The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+186x^78+348x^79+985x^80+1268x^81+2288x^82+2496x^83+3611x^84+3308x^85+4056x^86+3560x^87+3589x^88+2300x^89+2034x^90+1108x^91+752x^92+328x^93+242x^94+100x^95+94x^96+24x^97+44x^98+4x^99+15x^100+4x^101+12x^102+3x^104+2x^106+6x^108

The gray image is a code over GF(2) with n=688, k=15 and d=312.
This code was found by Heurico 1.16 in 19.1 seconds.