The generator matrix

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

generates a code of length 86 over Z16 who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+704x^82+986x^84+808x^86+950x^88+584x^90+12x^92+24x^94+24x^98+1x^100+1x^116+1x^128

The gray image is a code over GF(2) with n=688, k=12 and d=328.
This code was found by Heurico 1.16 in 27.7 seconds.