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

generates a code of length 79 over F9[X]/(X^2) who´s minimum homogenous weight is 615.

Homogenous weight enumerator: w(x)=1x^0+1080x^615+3240x^620+3256x^621+2016x^622+2592x^623+6264x^624+5184x^629+3240x^630+1152x^631+648x^632+3672x^633+9072x^638+5776x^639+2664x^640+2592x^641+6480x^642+80x^648+24x^657+8x^666+8x^675

The gray image is a linear code over GF(9) with n=711, k=5 and d=615.
This code was found by Heurico 1.16 in 1.65 seconds.