The generator matrix

 1  0  1
 0  1 a^7*X+1

generates a code of length 3 over F9[X]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+216x^16+24x^18+4536x^24+1728x^25+56x^27

The gray image is a linear code over GF(9) with n=27, k=4 and d=16.
This code was found by Heurico 1.16 in 8.11e-005 seconds.