The generator matrix

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

generates a code of length 99 over GR(64,4) who´s minimum homogenous weight is 684.

Homogenous weight enumerator: w(x)=1x^0+1176x^684+343x^688+784x^692+98x^696+1624x^700+49x^720+14x^728+7x^736

The gray image is a code over GF(8) with n=792, k=4 and d=684.
This code was found by Heurico 1.16 in 0.182 seconds.