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

generates a code of length 45 over F9[X]/(X^2) who´s minimum homogenous weight is 333.

Homogenous weight enumerator: w(x)=1x^0+720x^333+1200x^342+1032x^351+53496x^360+856x^369+872x^378+528x^387+272x^396+72x^405

The gray image is a linear code over GF(9) with n=405, k=5 and d=333.
This code was found by Heurico 1.16 in 1.87 seconds.