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

generates a code of length 64 over GR(64,4) who´s minimum homogenous weight is 424.

Homogenous weight enumerator: w(x)=1x^0+602x^424+868x^432+588x^440+29246x^448+385x^456+329x^464+266x^472+238x^480+147x^488+49x^496+28x^504+21x^512

The gray image is a code over GF(8) with n=512, k=5 and d=424.
This code was found by Heurico 1.16 in 38.7 seconds.