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  X  1  1  1  1  1  1
 0  X  0  X a*X a*X a^2*X a^5*X  0  X a*X 2*X a^2*X 2*X a^2*X a^3*X a^5*X 2*X  0 a*X a^3*X a^3*X a^2*X a^5*X  X a^3*X 2*X  0 a^5*X a*X a^2*X  X a^5*X  X a^6*X a^6*X a^6*X a^6*X  0  X
 0  0  X a^7*X a*X a^2*X a^6*X a^7*X a^3*X a^6*X 2*X a*X 2*X a^2*X  0  0 a^6*X 2*X a^2*X a^6*X a^7*X a^5*X a^5*X a^3*X a^5*X 2*X  0 a^5*X a*X a^7*X a^2*X a^3*X 2*X 2*X a^5*X a^3*X a*X a^7*X a*X a^6*X

generates a code of length 40 over F9[X]/(X^2) who´s minimum homogenous weight is 306.

Homogenous weight enumerator: w(x)=1x^0+88x^306+648x^312+408x^315+5184x^321+152x^324+24x^351+56x^360

The gray image is a linear code over GF(9) with n=360, k=4 and d=306.
This code was found by Heurico 1.16 in 0.0166 seconds.