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

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+664x^513+216x^515+360x^516+1736x^522+2808x^523+11160x^524+6048x^525+5536x^531+11016x^532+33264x^533+15984x^534+19104x^540+39528x^541+103248x^542+41760x^543+29856x^549+51624x^550+114552x^551+40824x^552+624x^558+664x^567+392x^576+248x^585+168x^594+56x^603

The gray image is a linear code over GF(9) with n=612, k=6 and d=513.
This code was found by Heurico 1.16 in 46.7 seconds.