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

generates a code of length 41 over F9[X]/(X^2) who´s minimum homogenous weight is 297.

Homogenous weight enumerator: w(x)=1x^0+232x^297+1024x^306+1136x^315+1104x^324+52488x^328+1048x^333+872x^342+616x^351+448x^360+80x^369

The gray image is a linear code over GF(9) with n=369, k=5 and d=297.
This code was found by Heurico 1.16 in 0.799 seconds.