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

generates a code of length 50 over F9[X]/(X^2) who´s minimum homogenous weight is 369.

Homogenous weight enumerator: w(x)=1x^0+352x^369+1096x^378+1104x^387+5832x^392+1008x^396+46656x^401+936x^405+784x^414+608x^423+448x^432+152x^441+72x^450

The gray image is a linear code over GF(9) with n=450, k=5 and d=369.
This code was found by Heurico 1.16 in 0.997 seconds.