The generator matrix

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

generates a code of length 16 over F9[X]/(X^2) who´s minimum homogenous weight is 121.

Homogenous weight enumerator: w(x)=1x^0+1152x^121+64x^126+1296x^128+4032x^130+16x^144

The gray image is a linear code over GF(9) with n=144, k=4 and d=121.
This code was found by Heurico 1.16 in 0.00958 seconds.