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

generates a code of length 75 over GR(64,4) who´s minimum homogenous weight is 512.

Homogenous weight enumerator: w(x)=1x^0+1596x^512+1120x^514+6272x^517+4718x^520+2240x^522+1792x^525+1330x^528+3808x^530+6272x^533+3542x^536+35x^544+28x^552+14x^560

The gray image is a code over GF(8) with n=600, k=5 and d=512.
This code was found by Heurico 1.16 in 0.326 seconds.