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

generates a code of length 83 over GR(64,4) who´s minimum homogenous weight is 552.

Homogenous weight enumerator: w(x)=1x^0+266x^552+791x^560+707x^568+623x^576+28672x^581+385x^584+385x^592+287x^600+203x^608+140x^616+126x^624+91x^632+49x^640+21x^648+14x^656+7x^664

The gray image is a code over GF(8) with n=664, k=5 and d=552.
This code was found by Heurico 1.16 in 0.949 seconds.