The generator matrix

 1  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  1  1  1  1 2a  1  1  1  1  1  1  1  1 2a^2  1  1  1  1  1  1  1  1 2a+2  1  1  1  1  1  1  1  1 2a^2+2a  1  1  1  1  1  1  1  1 2a^2+2a+2  1  1  1  1  1  1  1  1 2a^2+2  1  1  1  1  1  1  1  1  1  1
 0  1 2a^2+3  a 3a^2+2 2a^2+3a+1 a^2+3a a^2+3a+3 3a^2+2a+3  2 2a^2+2a+3 a+2 3a^2+2a+2 2a^2+3a+3 a^2+a a^2+3a+1 3a^2+3  1 2a 2a^2+2a+1 3a 3a^2+2a 2a^2+a+1 a^2+a+2 a^2+a+3 3a^2+1  1 2a^2 2a+3 2a^2+a a^2+2a+2 3a+1 3a^2+a 3a^2+3a+3 a^2+3  1 2a+2 2a^2+1 3a+2 3a^2 2a^2+a+3 a^2+3a+2 a^2+a+1 3a^2+2a+1  1 2a^2+2a 2a+1 2a^2+3a a^2+2a a+1 3a^2+a+2 3a^2+a+3 a^2+1  1 2a^2+2a+2  3 2a^2+3a+2 a^2+2 a+3 3a^2+3a 3a^2+a+1 a^2+2a+3  1 2a^2+2  1 2a^2+a+2 a^2 3a+3 3a^2+3a+2 3a^2+3a+1 a^2+2a+1  1  0 2a^2+3  a  2 2a^2+2a+3 a+2 3a^2+2 3a^2+2a+2 2a 2a^2+2a+1

generates a code of length 82 over GR(64,4) who´s minimum homogenous weight is 568.

Homogenous weight enumerator: w(x)=1x^0+238x^568+336x^569+2240x^574+686x^576+560x^577+35x^592

The gray image is a code over GF(8) with n=656, k=4 and d=568.
This code was found by Heurico 1.16 in 0.0798 seconds.