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

generates a code of length 81 over GR(64,4) who´s minimum homogenous weight is 536.

Homogenous weight enumerator: w(x)=1x^0+168x^536+686x^544+777x^552+4214x^560+25578x^568+357x^576+203x^584+210x^592+182x^600+154x^608+126x^616+84x^624+14x^632+14x^640

The gray image is a code over GF(8) with n=648, k=5 and d=536.
This code was found by Heurico 1.16 in 0.922 seconds.