The generator matrix

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

generates a code of length 64 over GR(64,4) who´s minimum homogenous weight is 416.

Homogenous weight enumerator: w(x)=1x^0+98x^416+56x^422+112x^423+1484x^424+1232x^425+840x^430+1456x^431+8715x^432+8288x^433+3864x^438+4368x^439+21182x^440+16128x^441+11032x^446+11536x^447+46501x^448+34720x^449+12880x^454+11200x^455+39711x^456+25648x^457+343x^464+266x^472+210x^480+175x^488+84x^496+14x^504

The gray image is a code over GF(8) with n=512, k=6 and d=416.
This code was found by Heurico 1.16 in 15.2 seconds.