The generator matrix

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

generates a code of length 13 over F9[X]/(X^2) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+288x^81+1944x^88+1136x^90+40824x^96+31104x^97+1104x^99+326592x^105+124416x^106+2696x^108+1336x^117

The gray image is a linear code over GF(9) with n=117, k=6 and d=81.
This code was found by Heurico 1.16 in 4.78 seconds.