The generator matrix

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

generates a code of length 65 over F9[X]/(X^2) who´s minimum homogenous weight is 502.

Homogenous weight enumerator: w(x)=1x^0+216x^502+112x^504+864x^506+720x^507+1080x^508+4536x^509+3888x^510+1872x^511+272x^513+3456x^515+1800x^516+1728x^517+4536x^518+2592x^519+1440x^520+144x^522+7344x^524+3312x^525+3024x^526+8424x^527+5184x^528+2304x^529+104x^531+40x^540+24x^549+24x^558+8x^567

The gray image is a linear code over GF(9) with n=585, k=5 and d=502.
This code was found by Heurico 1.16 in 0.499 seconds.