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
 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  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 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 a^7*X

generates a code of length 40 over F9[X]/(X^2) who´s minimum homogenous weight is 288.

Homogenous weight enumerator: w(x)=1x^0+240x^288+848x^297+1232x^306+1096x^315+52488x^320+968x^324+840x^333+752x^342+496x^351+88x^360

The gray image is a linear code over GF(9) with n=360, k=5 and d=288.
This code was found by Heurico 1.16 in 0.765 seconds.