The generator matrix

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

generates a code of length 46 over F9[X]/(X^2) who´s minimum homogenous weight is 342.

Homogenous weight enumerator: w(x)=1x^0+936x^342+1048x^351+1120x^360+52488x^368+976x^369+896x^378+704x^387+536x^396+296x^405+48x^414

The gray image is a linear code over GF(9) with n=414, k=5 and d=342.
This code was found by Heurico 1.16 in 78.3 seconds.