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

generates a code of length 90 over GR(64,4) who´s minimum homogenous weight is 600.

Homogenous weight enumerator: w(x)=1x^0+224x^600+56x^601+56x^602+56x^605+896x^607+2359x^608+3640x^609+1792x^610+1680x^613+5208x^615+7133x^616+10864x^617+4032x^618+4032x^621+11256x^623+12103x^624+18928x^625+6160x^626+11760x^629+22792x^631+23506x^632+32984x^633+11144x^634+11144x^637+17192x^639+15176x^640+19544x^641+5488x^642+280x^648+147x^656+154x^664+147x^672+63x^680+56x^688+56x^696+35x^704

The gray image is a code over GF(8) with n=720, k=6 and d=600.
This code was found by Heurico 1.16 in 23.3 seconds.