The generator matrix

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

generates a code of length 16 over F9[X]/(X^2) who´s minimum homogenous weight is 113.

Homogenous weight enumerator: w(x)=1x^0+864x^113+256x^117+2592x^120+6048x^122+192x^126+11664x^128+20736x^129+16416x^131+128x^135+152x^144

The gray image is a linear code over GF(9) with n=144, k=5 and d=113.
This code was found by Heurico 1.16 in 0.0797 seconds.