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

generates a code of length 74 over F9[X]/(X^2) who´s minimum homogenous weight is 558.

Homogenous weight enumerator: w(x)=1x^0+328x^558+1048x^567+1096x^576+1112x^585+52488x^592+664x^594+664x^603+568x^612+360x^621+344x^630+192x^639+144x^648+32x^657+8x^666

The gray image is a linear code over GF(9) with n=666, k=5 and d=558.
This code was found by Heurico 1.16 in 1.58 seconds.