The generator matrix

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

generates a code of length 83 over GR(64,4) who´s minimum homogenous weight is 568.

Homogenous weight enumerator: w(x)=1x^0+539x^568+1344x^569+9408x^573+1624x^576+2912x^577+2688x^581+735x^584+896x^585+9408x^589+1155x^592+2016x^593+42x^600

The gray image is a code over GF(8) with n=664, k=5 and d=568.
This code was found by Heurico 1.16 in 0.387 seconds.