The generator matrix

 1  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1  1  1  1  1  X  1  1  X  1  1  1  1 a^3*X  1  1  1  1  1  1  1  1 a^6*X  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1  1  1  1  1  1  1  1
 0  1  1  a a^7*X+a^2 a^3 a^7*X+2 a^7*X+a^6 a^5 a^7  0 a^7 a^5  a a^7*X+a^6 a^7*X+1 a^7*X+a^2 a^3 a^7*X+2  1  0 a^7*X+a^6 a^7 a^5 a^3  a a^7*X+2 a^7*X+a^2 X+a^7  X a^7*X+1 a^6*X+2  1 a^6*X+a^2 a*X a^7*X+1 X+a a^6*X+2 a^6*X+a^6 a^2*X+a  1 a^6*X+1 X+a^3  1 a^6*X+a^2 a^6*X+a^2 X+a^5 a*X+a^3  1 a^6*X+2 X+a^7 a^2*X+a^5 a^6*X+a^6 X+a^5 a^5*X a^6*X+a^6 a^2*X+a^7  1 a*X+2 X+a^3 a^2*X 2*X+a^7 a*X+2 a^6*X+a^6 2*X+a^5 a^5*X+1 a*X+1 2*X+a^6  0  1 a^3*X+a^6 a^5*X+2 X+a^5 X+1 a*X+a^2 2*X+a^6 X+a^5 a^7*X+a^2 a^7*X+1  0
 0  0 a^7*X  0 a^7*X  X a^6*X a^6*X 2*X a*X a^7*X a*X  X  0 a^5*X a^3*X a^6*X 2*X a^3*X  0 a^5*X a^3*X a^5*X a^3*X 2*X a*X a^2*X a^5*X a^7*X  X a*X  0 a^2*X a^6*X a*X  0 a^5*X  X a^3*X 2*X 2*X  0 a^5*X a^2*X  X a^7*X a^2*X a^3*X a*X  X 2*X 2*X a^2*X  0 a*X a^2*X  0 a^3*X a^3*X a^3*X a^7*X 2*X a^7*X 2*X a^5*X a*X a^7*X a^5*X a*X a^6*X 2*X a^3*X  0 a*X a*X a^6*X a^3*X a^6*X a^5*X  0
 0  0  0  X a^7*X a^7*X  X a*X  X a^2*X a^5*X a^6*X a^5*X a*X a^2*X a^7*X  0 a^3*X a*X a^3*X a^6*X a^6*X 2*X a^3*X a*X  X  X a^5*X a*X  0  0 a^6*X a^6*X 2*X a*X a^5*X a^7*X a^3*X 2*X a^6*X 2*X a^6*X  0 a*X 2*X  0 2*X  X a^3*X a^5*X  X a^6*X a^5*X  X 2*X a^3*X  0 2*X a^2*X  0 a^2*X a*X a*X a^3*X a*X a^2*X  X 2*X a^5*X a^3*X a*X 2*X 2*X a^7*X  0 a^7*X a^6*X  X  0  0

generates a code of length 80 over F9[X]/(X^2) who´s minimum homogenous weight is 603.

Homogenous weight enumerator: w(x)=1x^0+152x^603+72x^604+72x^611+1264x^612+2664x^613+936x^614+720x^618+1440x^619+2160x^620+7408x^621+15480x^622+4464x^623+4320x^627+5400x^628+6696x^629+16624x^630+35352x^631+10152x^632+18360x^636+19872x^637+20664x^638+42936x^639+81792x^640+20880x^641+29088x^645+25776x^646+22896x^647+41272x^648+74592x^649+16056x^650+536x^657+440x^666+352x^675+224x^684+216x^693+80x^702+32x^711

The gray image is a linear code over GF(9) with n=720, k=6 and d=603.
This code was found by Heurico 1.16 in 47.3 seconds.