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

generates a code of length 84 over GR(64,4) who´s minimum homogenous weight is 560.

Homogenous weight enumerator: w(x)=1x^0+322x^560+882x^568+672x^576+553x^584+28672x^588+413x^592+343x^600+266x^608+217x^616+126x^624+119x^632+84x^640+70x^648+21x^656+7x^672

The gray image is a code over GF(8) with n=672, k=5 and d=560.
This code was found by Heurico 1.16 in 0.957 seconds.