The generator matrix

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

generates a code of length 79 over F9[X]/(X^2) who´s minimum homogenous weight is 613.

Homogenous weight enumerator: w(x)=1x^0+5616x^613+23688x^614+3600x^615+1080x^620+56x^621+31536x^622+79704x^623+11376x^624+1728x^629+464x^630+44496x^631+113616x^632+11808x^633+3024x^638+192x^639+58320x^640+127080x^641+14040x^642+8x^657+8x^711

The gray image is a linear code over GF(9) with n=711, k=6 and d=613.
This code was found by Heurico 1.16 in 40.4 seconds.