The generator matrix

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

generates a code of length 73 over GR(64,4) who´s minimum homogenous weight is 503.

Homogenous weight enumerator: w(x)=1x^0+12544x^503+2016x^504+3584x^511+511x^512+12544x^519+1568x^520

The gray image is a code over GF(8) with n=584, k=5 and d=503.
This code was found by Heurico 1.16 in 17.7 seconds.