The generator matrix

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

generates a code of length 45 over F9[X]/(X^2) who´s minimum homogenous weight is 342.

Homogenous weight enumerator: w(x)=1x^0+64x^342+72x^344+648x^345+864x^346+2160x^348+2952x^349+264x^351+1152x^353+4536x^354+3456x^355+3456x^357+3168x^358+200x^360+4608x^362+12312x^363+7344x^364+6048x^366+5544x^367+88x^369+40x^378+40x^387+16x^396+16x^405

The gray image is a linear code over GF(9) with n=405, k=5 and d=342.
This code was found by Heurico 1.16 in 0.311 seconds.