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

generates a code of length 84 over GR(64,4) who´s minimum homogenous weight is 568.

Homogenous weight enumerator: w(x)=1x^0+2555x^568+2744x^569+448x^570+840x^571+896x^572+1568x^573+1904x^574+7224x^575+16618x^576+9856x^577+3976x^578+4256x^579+4872x^580+4648x^581+2408x^582+10472x^583+20125x^584+13048x^585+6832x^586+7784x^587+5488x^588+6160x^589+2912x^590+11592x^591+24325x^592+14896x^593+10248x^594+8624x^595+6664x^596+5544x^597+3528x^598+10136x^599+19187x^600+9632x^601+35x^608+42x^616+42x^624+7x^632+7x^640

The gray image is a code over GF(8) with n=672, k=6 and d=568.
This code was found by Heurico 1.16 in 17.9 seconds.