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  X  1  1  1  1  1  1  1  X  1  1  1  1 a^2*X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1 a^4*X  1 a^3*X  1  1  1  1  1  1 a^2*X  1  1  1  1  1  1 a*X  1  1
 0  1  1  a a^6*X+a^2 a^3 a^6*X+a^4 a^5 a^6*X+a^6  a a^6*X+a^2 a^6*X+a^4  1  0 a^3 a^6*X+a^6 a^6*X+1 a^5 a^6*X+a^6  a  1 a^6*X+a^4  0 a^6*X+a^2 a^5 X+a^3 a^5*X+a^2 a^6*X+1  X a^3 X+a^3 a^5*X+a^6  1 a^5*X+a^6  X a^4*X a^5*X+a^2 X+a X+a^5 a^5*X+a^4  1 a^4*X+a^4  X X+a^3 a*X+a^6  1 a^5*X+a^2 a^6*X+1 a^4*X+a^4  X X+a a*X+a a*X+a^5 a^2 a^5*X+1 a^6*X+a^6 X+a a^5*X+a^5 a^6*X+a^2 a^5*X+1  1 a^4*X+a^4 a^2*X+a^5  1 a^5*X+a a^2 a^5*X+1 a^5*X+1 a*X+a^3 a^2*X X+a^4  1 a^5*X+a^6  1 a^3*X+a^4 a^4*X+a^3 a*X+a a^6*X+1 a^3*X a^3*X+a^4  1 a^2*X+a^6 a*X+1 a^3*X+a^2 a^3*X+a a^4*X+a a^6*X+a  1 X+a^3  0
 0  0 a^6*X  0  X  X a^3*X  X a^2*X a^3*X a^6*X a^2*X  X a^4*X a^5*X  0 a^6*X  X a^5*X a*X a*X a^4*X a^3*X  X a^5*X a^6*X a^5*X a^5*X a^4*X  X a^4*X a^4*X a^4*X  0  X  0 a^2*X  0 a^3*X a^2*X a^4*X a^6*X  0 a^2*X a^2*X  X a^6*X a^6*X a^3*X a^5*X a^2*X a^4*X a^2*X a^3*X a^2*X  X a^3*X a^5*X  0 a^4*X a^4*X a^4*X  0 a^3*X  X a^3*X a^2*X  X a^5*X  X a^2*X  X a^5*X a^3*X  0 a^3*X  X a^4*X a*X a^6*X a*X  0 a^6*X a^5*X a^6*X a^2*X a^5*X a^3*X a^2*X a^2*X
 0  0  0  X a^6*X a^5*X a^3*X a^2*X a^5*X a^6*X a^6*X a^6*X a^5*X a^3*X a^3*X a^2*X a^2*X a*X a^2*X  X  0 a^4*X a*X  X a*X a^4*X a^6*X  X  0 a*X  X a^5*X a*X a*X a^5*X a^3*X  X a^4*X  X a^3*X a^3*X a^5*X a^5*X  0 a^3*X  0 a*X a^4*X a^5*X a^4*X a^6*X a^4*X a^4*X a*X a^5*X a^3*X a^2*X a^2*X a^2*X a^5*X a*X  X a^4*X a*X a^2*X  X a^4*X a*X  0 a^3*X  0 a*X a*X a^5*X  0 a^3*X a^6*X a^6*X a^5*X a^4*X  X  X  X a^4*X a*X a^5*X a^4*X a^4*X a^6*X a*X

generates a code of length 90 over F8[X]/(X^2) 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 linear code over GF(8) with n=720, k=6 and d=600.
This code was found by Heurico 1.16 in 23 seconds.