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  2  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  2  1  1  1  1  2
 0 12  0  4  0  0  4 12  0  0  4 12  0  0  4 12  0  0  4 12  0  0  4 12  0  0  4 12  8 12  8  8  8  4  8 12  4 12  4  8  8 12  4  8  8 12  4  8  8  0  0 12  4  8  8 12  4  8  8 12  4  8  8 12  4  0  0  4 12  0  0  4 12  0  8  4  4  8 12  0 12  4 12  4 12 12 12
 0  0 12  4  0 12  4  0  0 12  4  0  0 12  4  0  8  4 12  8  8  4 12  8  8  4 12  8  8  8  4 12  0 12  4 12  8 12  8  8  4 12  8  8  4 12  8  8  4  8  4  4  0  0 12  4  0  0 12  4  0  0 12  4  0  0 12  4  0  0 12 12  8  0  4  4  8  8  4  8  0 12 12  0 12  4  0
 0  0  0  8  0  0  8  0  8  8  0  8  8  8  0  8  8  8  8  8  8  8  8  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  0  0  8  8  8  8  0  0  8  8  8  8  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  0  8  0  8
 0  0  0  0  8  8  8  8  8  8  0  8  0  0  8  0  0  0  0  0  8  8  8  8  8  8  8  8  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  0  0  0  0  8  8  8  8  8  0  8  0  0  0  8  8  0  0  8  8  0  0

generates a code of length 87 over Z16 who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+97x^84+48x^85+24x^86+672x^87+82x^88+48x^89+8x^90+43x^92+1x^168

The gray image is a code over GF(2) with n=696, k=10 and d=336.
This code was found by Heurico 1.16 in 98.1 seconds.