The generator matrix

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

generates a code of length 14 over F9[X]/(X^2) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+992x^81+3048x^90+7008x^99+52488x^104+17016x^108+419904x^113+19632x^117+11352x^126

The gray image is a linear code over GF(9) with n=126, k=6 and d=81.
This code was found by Heurico 1.16 in 14.6 seconds.