The generator matrix

 1  0  1  1  1  1  1
 0  1  1  2  0  X  0
 0  0 2X  0  X 2X  0
 0  0  0  X  X 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+34x^9+234x^12+396x^15+64x^18

The gray image is a linear code over GF(3) with n=21, k=6 and d=9.
This code was found by Heurico 1.16 in 0.000472 seconds.