The generator matrix

 1  0  1  1  1  1  1  1  1  1  1  1  0  1  1  1  1  1  1  1  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  1  1  2  1  1  1  1  1  1  1  1 2a  1  1  1  1  1  1  1  1  1  1 2a^2+2a  1  1  1  1  2  1  1  1  1  1  1  1  2  1  1  1  2  1  1
 0  1  1  a 3a^2+2 2a^2+3a+1 a^2+3a a^2+3a+3 3a^2+2a+3  a 3a^2+2 a^2+3a  1  0 2a^2+3a+1 3a^2+2a+3 2a^2+3 a^2+3a+3 3a^2+2a+3  a  1 a^2+3a  0 3a^2+2 a^2+3a+3 2a^2+3a+3 3a^2+2a+2 2a^2+3 3a^2+2a+2 2a^2+3a+1 a^2+a a^2+3a+1  2 a^2+a 3a^2+3  1 3a+1 a+2 2a^2+3 a+2 2a^2+a+3 2a^2+2a+1  1 a^2+3a+1  2 3a^2+1 a^2+a 2a^2+2a+3 a^2+2 a+2 3a^2+3a+3  1 3a+2  2 a+3 a^2+1 3a^2+2a+2 a^2+a+2 3a^2+3 3a^2+3a+1  a  2  1 a^2+a+2 a^2+2a+2 2a+3 a^2+a+3  1 2a^2+3 3a^2 a^2+2a+1 3a+1  1 a^2 a^2+1 2a+2 2a+1 3a^2+2a+2 3a+1  1 a+2  0
 0  0 2a^2+2  0  2  2 2a+2  2 2a^2 2a+2 2a^2+2 2a^2  2 2a^2+2a 2a^2+2a+2  0 2a^2+2  2 2a^2+2a+2 2a 2a 2a^2+2a 2a+2  2 2a^2+2a+2 2a^2+2 2a^2+2a+2 2a^2+2a+2 2a^2+2 2a^2+2a 2a^2+2a 2a^2+2a+2 2a^2+2 2a 2a^2+2a 2a 2a^2+2a+2  0  0  2 2a^2+2  0  2 2a^2 2a^2+2a+2 2a^2 2a^2+2a 2a^2+2a  0  2 2a^2+2a 2a+2 2a^2 2a+2  2  0 2a 2a^2 2a^2 2a^2+2a+2  0 2a^2+2a+2 2a^2+2a+2  2 2a 2a^2 2a+2 2a^2+2a+2 2a^2 2a^2+2a+2 2a^2+2a+2 2a+2  0  2  0 2a^2 2a^2+2a 2a+2 2a+2 2a^2+2a 2a+2 2a
 0  0  0  2 2a^2+2 2a^2+2a+2 2a+2 2a^2 2a^2+2a+2 2a^2+2 2a^2+2 2a^2+2 2a^2+2a+2 2a+2 2a+2 2a^2 2a^2 2a 2a^2  2  0 2a^2+2a 2a  2 2a 2a^2+2a 2a^2+2  2 2a 2a+2 2a^2+2a+2 2a^2  0 2a^2  2 2a+2 2a^2+2a 2a^2+2 2a^2+2a 2a+2 2a+2  0  0  0 2a^2+2a 2a+2  2 2a 2a 2a  0 2a^2  2  0  0  2 2a^2 2a^2+2a+2 2a^2  0 2a^2+2a 2a^2+2a+2 2a^2+2a 2a^2+2a 2a 2a 2a^2+2a+2 2a^2 2a^2+2  2 2a+2 2a^2+2a+2 2a^2 2a^2+2a+2  0 2a+2 2a^2+2a+2 2a+2 2a 2a 2a+2  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+182x^544+112x^546+1568x^551+3920x^552+1288x^553+1568x^554+7336x^559+13020x^560+3472x^561+3976x^562+16968x^567+25396x^568+6496x^569+7112x^570+34552x^575+44730x^576+10864x^577+10024x^578+25592x^583+30604x^584+6552x^585+5880x^586+238x^592+273x^600+119x^608+105x^616+63x^624+63x^632+56x^640+7x^648+7x^656

The gray image is a code over GF(8) with n=656, k=6 and d=544.
This code was found by Heurico 1.16 in 20 seconds.