The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  2  0  0  2  2 2a  0 2a^2 2a^2 2a^2 2a^2  2 2a^2+2a 2a+2 2a^2+2a+2
 0  0  2  0 2a^2+2 2a^2+2a+2 2a 2a+2 2a^2+2 2a^2 2a^2+2a 2a^2+2 2a^2+2  0 2a^2+2a+2 2a+2
 0  0  0  2  2 2a^2+2a 2a^2+2a 2a+2 2a^2+2a  2 2a 2a 2a 2a^2 2a^2+2a  2

generates a code of length 16 over GR(64,4) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+868x^96+448x^104+29680x^112+1344x^120+427x^128

The gray image is a code over GF(8) with n=128, k=5 and d=96.
This code was found by Heurico 1.16 in 12.6 seconds.