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

generates a code of length 31 over F9[X]/(X^2) who´s minimum homogenous weight is 216.

Homogenous weight enumerator: w(x)=1x^0+136x^216+912x^225+984x^234+5832x^240+1128x^243+46656x^249+1200x^252+1104x^261+904x^270+192x^279

The gray image is a linear code over GF(9) with n=279, k=5 and d=216.
This code was found by Heurico 1.16 in 0.555 seconds.