The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+34x^79+136x^80+476x^81+505x^82+748x^83+757x^84+1084x^85+876x^86+1034x^87+727x^88+792x^89+376x^90+330x^91+157x^92+76x^93+27x^94+26x^95+10x^96+4x^97+6x^98+2x^103+2x^104+2x^107+2x^108+1x^114+1x^126

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 1.74 seconds.