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  2  2  2  1  1  1  1  2  2  2  1  1  1  2  2  2  1  1  1  2  2  2  2  4  4  4  1  1  2  2  2  2  1  2  4  4  4  1  1  8  8  8  2  0  0  0  4  1  2  4  4  4  4  2  2  2  1  1
 0  8  0  8  0  0  8  8  0  0  8  8  0  0  8  8  0  0  8  8  0  0  8  8  0  0  8  8  0  8  8  0  0  8  8  0  8  8  0  0  8  0  8  8  8  0  0  8  8  0  0  8  8  0  8  8  0  0  8  8  0  0  0  8  8  0  8  0  8  8  0  8  8  0  0  8  0  0  8  0  8  0  8  0  0  0
 0  0  8  8  0  8  8  0  0  8  8  0  0  8  8  0  0  8  8  0  0  8  8  0  0  8  8  0  8  8  0  0  8  8  0  8  8  0  0  8  8  8  8  0  0  0  8  8  0  0  8  8  0  8  8  0  0  8  8  0  0  0  8  8  0  8  8  8  8  0  0  0  8  8  0  0  0  8  8  0  0  8  8  0  0  0

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

Homogenous weight enumerator: w(x)=1x^0+34x^86+12x^87+3x^88+6x^90+4x^91+4x^92

The gray image is a code over GF(2) with n=688, k=6 and d=344.
This code was found by Heurico 1.16 in 0.409 seconds.