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

generates a code of length 71 over GR(64,4) who´s minimum homogenous weight is 472.

Homogenous weight enumerator: w(x)=1x^0+651x^472+721x^480+651x^488+469x^496+28672x^497+483x^504+329x^512+266x^520+224x^528+119x^536+105x^544+63x^552+7x^560+7x^568

The gray image is a code over GF(8) with n=568, k=5 and d=472.
This code was found by Heurico 1.16 in 44 seconds.