The generator matrix

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

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+160x^603+936x^612+1120x^621+1000x^630+816x^639+52488x^640+720x^648+488x^657+424x^666+336x^675+336x^684+120x^693+64x^702+32x^711+8x^720

The gray image is a linear code over GF(9) with n=720, k=5 and d=603.
This code was found by Heurico 1.16 in 1.75 seconds.