The generator matrix

 1  1  1  1  1  1  1
 0  X  0  0  X  0  X
 0  0  X  0 2X  X 2X
 0  0  0  X 2X 2X  X

generates a code of length 7 over Z3[X]/(X^2) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+12x^9+22x^12+162x^14+30x^15+8x^18+8x^21

The gray image is a linear code over GF(3) with n=21, k=5 and d=9.
This code was found by Heurico 1.16 in 0.000211 seconds.