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

generates a code of length 37 over F9[X]/(X^2) who´s minimum homogenous weight is 270.

Homogenous weight enumerator: w(x)=1x^0+696x^270+1104x^279+1176x^288+52488x^296+1080x^297+1008x^306+840x^315+536x^324+120x^333

The gray image is a linear code over GF(9) with n=333, k=5 and d=270.
This code was found by Heurico 1.16 in 0.664 seconds.