The generator matrix

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

generates a code of length 16 over F9[X]/(X^2) who´s minimum homogenous weight is 108.

Homogenous weight enumerator: w(x)=1x^0+896x^108+896x^117+1536x^126+52488x^128+2304x^135+928x^144

The gray image is a linear code over GF(9) with n=144, k=5 and d=108.
This code was found by Heurico 1.16 in 33.6 seconds.