The generator matrix

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

generates a code of length 15 over F9[X]/(X^2) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+336x^81+1584x^90+3576x^99+7960x^108+16056x^117+472392x^120+18168x^126+11368x^135

The gray image is a linear code over GF(9) with n=135, k=6 and d=81.
This code was found by Heurico 1.16 in 13.2 seconds.