The generator matrix

 1  0  1  1  1  1  1
 0  1  1  2  0  0  0
 0  0 2X  0  0  0  X
 0  0  0  X  0  0  X
 0  0  0  0  X  0  X
 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+60x^6+214x^9+2100x^12+3702x^15+442x^18+42x^21

The gray image is a linear code over GF(3) with n=21, k=8 and d=6.
This code was found by Heurico 1.16 in 0.00551 seconds.