The generator matrix

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

generates a code of length 7 over Z3[X]/(X^2) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+38x^6+102x^9+644x^12+1186x^15+194x^18+22x^21

The gray image is a linear code over GF(3) with n=21, k=7 and d=6.
This code was found by Heurico 1.16 in 0.00112 seconds.