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

generates a code of length 34 over F9[X]/(X^2) who´s minimum homogenous weight is 243.

Homogenous weight enumerator: w(x)=1x^0+224x^243+1184x^252+1192x^261+1040x^270+52488x^272+1064x^279+1064x^288+640x^297+152x^306

The gray image is a linear code over GF(9) with n=306, k=5 and d=243.
This code was found by Heurico 1.16 in 0.633 seconds.