The generator matrix

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

generates a code of length 78 over GR(64,4) who´s minimum homogenous weight is 517.

Homogenous weight enumerator: w(x)=1x^0+336x^517+448x^518+525x^520+280x^522+504x^523+1736x^524+3024x^525+2800x^526+784x^528+1736x^530+2408x^531+5600x^532+10920x^533+7616x^534+700x^536+5656x^538+5880x^539+13104x^540+19656x^541+15008x^542+476x^544+11032x^546+11256x^547+21728x^548+32424x^549+19712x^550+455x^552+9968x^554+8624x^555+15176x^556+19656x^557+11760x^558+392x^560+217x^568+147x^576+147x^584+119x^592+77x^600+42x^608+7x^616+7x^624

The gray image is a code over GF(8) with n=624, k=6 and d=517.
This code was found by Heurico 1.16 in 18.8 seconds.