The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1  4  1  2  2  1  1  1  1  1  1  1  1  1  1  0  1  2  1  1  8  1  1  2  2  1  1  1  1 12  1  0  1  1 12  1  2  4  1  2  8  1  2  2  1  1  1  2  1  1  2  4  1
 0  2  0  2  0  8  2 10  8  2 12 14  0 10  4  6  4  6  4 14 12  2  6  0  0  2  8 12 14  0  2 14 10 10 12  4 10 12 10  4 14  0 14 12 14 14  0  2  2  6  6  8  8  0 10  8  2  4  2 12 10 12 12  0  2  6  2  8 12  6  2  2  8  2  4 10 14 10  8 12  0 12 10 14  2  0
 0  0  2  2 12 14  6 12  0  2 10 12  4 14 14  8  4 10 10  4  4  8  6  6 10  8 14  8  2  4  0  8 14  2  2  2  4 14  6 10  0  8  4  8 12 10 10 12  6  6 14  4  4  2  2  6  6 14  4 12 14  0  2  4  6  0  8  2  6  2  0  8 10 12  0 12  6  8  2  6 14  0  2 14 14 12
 0  0  0  4  0  0 12  8  4  8 12 12 12  8  4 12  8  4  8  0 12 12  0  8  4  0  4  0 12 12  0  4  8  8  0  0  4  4 12  4  0  8  0  4  4  0  0  4  8 12  8  8  4  4  0  4  4  0  0 12  0  8  4  0  8  8  4 12  8  4 12  8  8  8  0  8 12 12 12  0 12 12 12  4 12  4
 0  0  0  0  8  8  8  8  0  0  0  8  8  8  8  0  0  8  0  0  8  0  8  8  8  8  0  8  0  0  8  8  0  8  0  0  8  8  0  8  0  8  8  8  8  8  8  0  8  8  8  8  0  0  0  8  8  8  0  0  8  8  8  0  0  8  8  8  0  0  8  8  8  0  0  0  8  8  8  8  0  8  0  8  0  0

generates a code of length 86 over Z16 who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+104x^79+283x^80+338x^81+560x^82+670x^83+919x^84+966x^85+1001x^86+738x^87+814x^88+578x^89+473x^90+244x^91+147x^92+116x^93+88x^94+44x^95+40x^96+32x^97+20x^98+6x^99+4x^100+2x^101+1x^102+2x^103+1x^130

The gray image is a code over GF(2) with n=688, k=13 and d=316.
This code was found by Heurico 1.16 in 2.43 seconds.