The generator matrix

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

generates a code of length 4 over F9[X]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+432x^16+48x^18+18144x^24+6912x^25+224x^27+332424x^32+145152x^33+27648x^34+456x^36

The gray image is a linear code over GF(9) with n=36, k=6 and d=16.
This code was found by Heurico 1.16 in 0.307 seconds.