The generator matrix

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

generates a code of length 4 over F9[X]/(X^2) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+32x^9+648x^16+384x^18+11664x^24+10368x^25+2048x^27+367416x^32+93312x^33+41472x^34+4096x^36

The gray image is a linear code over GF(9) with n=36, k=6 and d=9.
This code was found by Heurico 1.16 in 0.331 seconds.