The generator matrix

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

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+42x^6+70x^9+210x^12+1458x^14+210x^15+154x^18+42x^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 0.00165 seconds.