The generator matrix

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

generates a code of length 57 over F9[X]/(X^2) who´s minimum homogenous weight is 423.

Homogenous weight enumerator: w(x)=1x^0+232x^423+432x^427+1080x^432+288x^433+2808x^434+2808x^435+6048x^436+1096x^441+3024x^442+17496x^443+11016x^444+20088x^445+1064x^450+16416x^451+73224x^452+39528x^453+62424x^454+888x^459+32760x^460+116424x^461+51624x^462+68472x^463+696x^468+520x^477+544x^486+296x^495+128x^504+16x^513

The gray image is a linear code over GF(9) with n=513, k=6 and d=423.
This code was found by Heurico 1.16 in 32.5 seconds.