The generator matrix

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

generates a code of length 16 over F9[X]/(X^2) who´s minimum homogenous weight is 117.

Homogenous weight enumerator: w(x)=1x^0+256x^117+192x^126+5832x^128+128x^135+152x^144

The gray image is a linear code over GF(9) with n=144, k=4 and d=117.
This code was found by Heurico 1.16 in 0.00347 seconds.