The generator matrix

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

generates a code of length 77 over GR(64,4) who´s minimum homogenous weight is 533.

Homogenous weight enumerator: w(x)=1x^0+336x^533+21x^536+392x^538+2240x^539+1008x^541+56x^546+35x^552+7x^560

The gray image is a code over GF(8) with n=616, k=4 and d=533.
This code was found by Heurico 1.16 in 1.27 seconds.