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

generates a code of length 55 over F9[X]/(X^2) who´s minimum homogenous weight is 405.

Homogenous weight enumerator: w(x)=1x^0+104x^405+72x^411+720x^413+864x^414+792x^417+2088x^418+2880x^419+2088x^420+3528x^422+1280x^423+9288x^426+13176x^427+10800x^428+6912x^429+8424x^431+984x^432+49032x^435+54864x^436+39744x^437+20448x^438+22176x^440+792x^441+98352x^444+87336x^445+51552x^446+22968x^447+17640x^449+888x^450+656x^459+504x^468+304x^477+160x^486+24x^495

The gray image is a linear code over GF(9) with n=495, k=6 and d=405.
This code was found by Heurico 1.16 in 31.1 seconds.