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

generates a code of length 82 over GR(64,4) who´s minimum homogenous weight is 567.

Homogenous weight enumerator: w(x)=1x^0+2016x^567+252x^568+63x^576+1568x^583+196x^584

The gray image is a code over GF(8) with n=656, k=4 and d=567.
This code was found by Heurico 1.16 in 15.1 seconds.