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

generates a code of length 78 over F9[X]/(X^2) who´s minimum homogenous weight is 585.

Homogenous weight enumerator: w(x)=1x^0+80x^585+744x^594+504x^595+144x^596+864x^597+936x^598+1168x^603+12384x^604+3384x^605+7920x^606+4464x^607+1000x^612+41472x^613+7128x^614+17712x^615+10152x^616+832x^621+122832x^622+21672x^623+42336x^624+20880x^625+688x^630+137736x^631+20160x^632+36144x^633+16056x^634+656x^639+416x^648+440x^657+224x^666+192x^675+104x^684+8x^693+8x^702

The gray image is a linear code over GF(9) with n=702, k=6 and d=585.
This code was found by Heurico 1.16 in 47.7 seconds.