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

generates a code of length 82 over GR(64,4) who´s minimum homogenous weight is 544.

Homogenous weight enumerator: w(x)=1x^0+168x^544+742x^552+742x^560+3584x^567+728x^568+25088x^575+420x^576+378x^584+203x^592+175x^600+210x^608+112x^616+105x^624+91x^632+7x^640+14x^648

The gray image is a code over GF(8) with n=656, k=5 and d=544.
This code was found by Heurico 1.16 in 0.937 seconds.