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

generates a code of length 85 over GR(64,4) who´s minimum homogenous weight is 568.

Homogenous weight enumerator: w(x)=1x^0+763x^568+56x^569+504x^571+3808x^575+5775x^576+840x^577+6888x^579+7560x^583+12376x^584+3864x^585+13944x^587+13608x^591+24906x^592+11032x^593+35448x^595+20888x^599+35056x^600+12880x^601+29232x^603+11480x^607+10332x^608+280x^616+161x^624+182x^632+105x^640+98x^648+49x^656+21x^664+7x^672

The gray image is a code over GF(8) with n=680, k=6 and d=568.
This code was found by Heurico 1.16 in 21 seconds.