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

generates a code of length 89 over GR(64,4) who´s minimum homogenous weight is 592.

Homogenous weight enumerator: w(x)=1x^0+140x^592+168x^596+280x^597+504x^599+2023x^600+1232x^602+2072x^604+2912x^605+6832x^607+8820x^608+3640x^610+4648x^612+4424x^613+14112x^615+16961x^616+6328x^618+6888x^620+7224x^621+35280x^623+35224x^624+10920x^626+9744x^628+9408x^629+29288x^631+25970x^632+6552x^634+5152x^636+4424x^637+280x^640+196x^648+112x^656+105x^664+112x^672+91x^680+56x^688+14x^696+7x^704

The gray image is a code over GF(8) with n=712, k=6 and d=592.
This code was found by Heurico 1.16 in 23.2 seconds.