The generator matrix

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

generates a code of length 90 over F8[X]/(X^2) who´s minimum homogenous weight is 610.

Homogenous weight enumerator: w(x)=1x^0+3416x^610+3584x^611+672x^613+896x^614+1232x^615+2009x^616+4872x^617+21448x^618+11256x^619+840x^620+2856x^621+4760x^622+3864x^623+4081x^624+8512x^625+29400x^626+14560x^627+1008x^628+4816x^629+5712x^630+4704x^631+4536x^632+7784x^633+29848x^634+15960x^635+1736x^636+5992x^637+6552x^638+4536x^639+4116x^640+7504x^641+26992x^642+11984x^643+28x^648+35x^656+28x^664+7x^672+7x^680

The gray image is a linear code over GF(8) with n=720, k=6 and d=610.
This code was found by Heurico 1.16 in 19.4 seconds.