The generator matrix

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

generates a code of length 87 over Z16 who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+160x^79+451x^80+762x^81+1301x^82+1902x^83+3046x^84+3278x^85+4077x^86+3422x^87+4012x^88+3154x^89+2693x^90+1800x^91+1274x^92+562x^93+357x^94+160x^95+139x^96+88x^97+18x^98+42x^99+32x^100+20x^101+2x^102+2x^103+2x^104+4x^105+4x^109+3x^112

The gray image is a code over GF(2) with n=696, k=15 and d=316.
This code was found by Heurico 1.16 in 23.4 seconds.