The generator matrix

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

generates a code of length 66 over F9[X]/(X^2) who´s minimum homogenous weight is 508.

Homogenous weight enumerator: w(x)=1x^0+4032x^508+9936x^509+2808x^510+488x^513+432x^514+1440x^515+6480x^516+40824x^517+44784x^518+9720x^519+3320x^522+1728x^523+3600x^524+10368x^525+65016x^526+72432x^527+18792x^528+8488x^531+3672x^532+6624x^533+18144x^534+94248x^535+88632x^536+15336x^537+48x^540+16x^549+8x^558+16x^567+8x^594

The gray image is a linear code over GF(9) with n=594, k=6 and d=508.
This code was found by Heurico 1.16 in 33 seconds.