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

generates a code of length 89 over Z16 who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+110x^84+80x^86+208x^88+1280x^89+160x^90+114x^92+80x^94+14x^96+1x^176

The gray image is a code over GF(2) with n=712, k=11 and d=336.
This code was found by Heurico 1.16 in 0.863 seconds.