The generator matrix

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

generates a code of length 68 over GR(64,4) who´s minimum homogenous weight is 467.

Homogenous weight enumerator: w(x)=1x^0+4704x^467+7840x^468+245x^472+3136x^475+2240x^476+231x^480+6496x^483+7840x^484+28x^488+7x^504

The gray image is a code over GF(8) with n=544, k=5 and d=467.
This code was found by Heurico 1.16 in 84.2 seconds.