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

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

Homogenous weight enumerator: w(x)=1x^0+224x^82+32x^83+398x^84+224x^85+436x^86+224x^87+222x^88+32x^89+152x^90+82x^92+20x^94+1x^160

The gray image is a code over GF(2) with n=688, k=11 and d=328.
This code was found by Heurico 1.16 in 71.6 seconds.