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

generates a code of length 42 over F9[X]/(X^2) who´s minimum homogenous weight is 306.

Homogenous weight enumerator: w(x)=1x^0+312x^306+1088x^315+1104x^324+1168x^333+52488x^336+1048x^342+712x^351+632x^360+408x^369+88x^378

The gray image is a linear code over GF(9) with n=378, k=5 and d=306.
This code was found by Heurico 1.16 in 0.812 seconds.