The generator matrix

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

generates a code of length 82 over GR(64,4) who´s minimum homogenous weight is 554.

Homogenous weight enumerator: w(x)=1x^0+3304x^554+56x^556+560x^557+2576x^558+3528x^559+6223x^560+5824x^561+17192x^562+616x^564+4200x^565+9744x^566+9296x^567+11263x^568+8848x^569+22344x^570+1288x^572+5600x^573+12208x^574+11144x^575+13300x^576+9184x^577+24920x^578+1624x^580+7560x^581+14896x^582+11872x^583+12614x^584+8400x^585+21840x^586+77x^592+35x^600+7x^608

The gray image is a code over GF(8) with n=656, k=6 and d=554.
This code was found by Heurico 1.16 in 44.1 seconds.