The generator matrix

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

generates a code of length 12 over F9[X]/(X^2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+224x^72+864x^81+1344x^90+52488x^96+2560x^99+1568x^108

The gray image is a linear code over GF(9) with n=108, k=5 and d=72.
This code was found by Heurico 1.16 in 0.141 seconds.