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

generates a code of length 77 over GR(64,4) who´s minimum homogenous weight is 512.

Homogenous weight enumerator: w(x)=1x^0+385x^512+819x^520+728x^528+3584x^532+581x^536+25088x^540+385x^544+364x^552+175x^560+280x^568+91x^576+161x^584+77x^592+35x^600+14x^608

The gray image is a code over GF(8) with n=616, k=5 and d=512.
This code was found by Heurico 1.16 in 0.853 seconds.