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

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

Homogenous weight enumerator: w(x)=1x^0+322x^552+168x^553+112x^556+280x^557+392x^558+1400x^559+770x^560+2968x^561+3248x^564+4760x^565+2520x^566+6944x^567+658x^568+8904x^569+8400x^572+9128x^573+5768x^574+11088x^575+644x^576+12936x^577+23184x^580+23688x^581+11592x^582+23072x^583+399x^584+20720x^585+22400x^588+19488x^589+8400x^590+14840x^591+357x^592+11648x^593+231x^600+259x^608+119x^616+105x^624+147x^632+56x^640+28x^648

The gray image is a code over GF(8) with n=664, k=6 and d=552.
This code was found by Heurico 1.16 in 20.1 seconds.