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

generates a code of length 84 over GR(64,4) who´s minimum homogenous weight is 560.

Homogenous weight enumerator: w(x)=1x^0+364x^560+56x^561+1176x^564+1232x^567+2429x^568+2464x^569+12936x^572+3752x^575+5005x^576+4200x^577+29400x^580+5992x^583+7168x^584+7000x^585+69720x^588+11256x^591+10878x^592+9856x^593+58800x^596+6440x^599+6034x^600+5096x^601+252x^608+140x^616+140x^624+161x^632+98x^640+84x^648+14x^656

The gray image is a code over GF(8) with n=672, k=6 and d=560.
This code was found by Heurico 1.16 in 20.3 seconds.