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

generates a code of length 68 over F9[X]/(X^2) who´s minimum homogenous weight is 513.

Homogenous weight enumerator: w(x)=1x^0+592x^513+1080x^522+1136x^531+5832x^536+984x^540+46656x^545+736x^549+552x^558+488x^567+512x^576+272x^585+128x^594+72x^603+8x^612

The gray image is a linear code over GF(9) with n=612, k=5 and d=513.
This code was found by Heurico 1.16 in 1.41 seconds.