The generator matrix

 1  1  1  1
 0  X  0  0
 0  0  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+384x^18+2048x^27+52488x^32+4096x^36

The gray image is a linear code over GF(9) with n=36, k=5 and d=9.
This code was found by Heurico 1.16 in 0.0103 seconds.