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

generates a code of length 44 over F9[X]/(X^2) who´s minimum homogenous weight is 324.

Homogenous weight enumerator: w(x)=1x^0+536x^324+1160x^333+1152x^342+1112x^351+52488x^352+856x^360+704x^369+664x^378+288x^387+88x^396

The gray image is a linear code over GF(9) with n=396, k=5 and d=324.
This code was found by Heurico 1.16 in 0.824 seconds.