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

generates a code of length 67 over F9[X]/(X^2) who´s minimum homogenous weight is 504.

Homogenous weight enumerator: w(x)=1x^0+384x^504+1136x^513+648x^520+1192x^522+10368x^529+1008x^531+41472x^538+752x^540+608x^549+504x^558+424x^567+272x^576+192x^585+72x^594+16x^603

The gray image is a linear code over GF(9) with n=603, k=5 and d=504.
This code was found by Heurico 1.16 in 1.4 seconds.