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
 0  X  0  0  X  X a*X a^2*X a^4*X a^5*X a^5*X  X a^5*X a^6*X  0 a*X a^5*X a*X a^5*X  0 a^4*X a*X a*X a^2*X a*X  X a^4*X a^2*X  X a^3*X a^6*X a^4*X  0  0 a^4*X a^2*X a^2*X a^6*X a^2*X a^3*X a^2*X a^5*X a^2*X a^5*X a^6*X a^4*X a*X a^4*X  X a^4*X  X a^5*X a*X  X a^3*X  X  0 a^2*X a^2*X a*X a^5*X a*X a^4*X a^3*X a^4*X a^2*X a^6*X a^6*X a*X a^6*X a*X  X  X a^4*X a^2*X a^2*X  X  0 a^3*X  0 a^4*X a^4*X a^5*X a^6*X a^6*X a^2*X a^5*X a^4*X a^2*X  0
 0  0  X  0 a^6*X a^5*X a*X a^6*X a^6*X a*X a^6*X a^2*X a*X a^3*X  X a^5*X  X  X a^4*X a^3*X  X a*X a^4*X  0 a^2*X  0  0 a^2*X a^2*X a^6*X  X a^5*X a^4*X a^6*X  X a^2*X  0 a^6*X a^2*X a^5*X  X a^2*X a^6*X a^5*X a^4*X a^5*X a^4*X a*X a^5*X  0 a^6*X a^2*X  X  0 a^3*X a^3*X a*X a^4*X a^4*X a^5*X a^4*X a^4*X  0 a^3*X a^3*X a^6*X a^4*X a^6*X  X a^5*X a^2*X a^3*X a^2*X a*X  X a*X a^5*X  0 a^5*X a^3*X a*X a^2*X a^5*X a^5*X  0  0 a*X a^5*X  X  0
 0  0  0  X  X a^4*X a^4*X  X a^6*X a^4*X a^6*X a^6*X a^3*X a*X a^4*X a*X a^3*X a^5*X a^6*X a^2*X a^4*X  X  0 a^5*X  0 a^5*X a*X a^6*X a^3*X  0 a^3*X a^6*X a^3*X a^4*X a^2*X a*X  0 a^4*X a^2*X  X a^2*X a^3*X  0 a^5*X a^3*X a^5*X a^2*X a^5*X a^3*X a^4*X a^6*X  0 a^2*X a*X a^2*X  X a^3*X a*X a^6*X a^3*X a^4*X a^3*X a^5*X a^5*X a^4*X a*X a^4*X  X a^3*X a^3*X a*X a^2*X a^5*X a^6*X  X a^4*X a*X a*X  0 a^4*X a^3*X a^2*X a^6*X a^4*X a^3*X a^2*X a*X  X a*X a^5*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+266x^600+756x^608+686x^616+567x^624+28672x^630+441x^632+364x^640+322x^648+217x^656+147x^664+161x^672+49x^680+35x^688+42x^696+28x^704+7x^712+7x^720

The gray image is a linear code over GF(8) with n=720, k=5 and d=600.
This code was found by Heurico 1.16 in 1.08 seconds.