The generator matrix

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

generates a code of length 7 over Z3[X]/(X^2) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+60x^4+312x^6+600x^7+1350x^8+2230x^9+8070x^10+8100x^11+18840x^12+27480x^13+32238x^14+33150x^15+27480x^16+10800x^17+4474x^18+1920x^19+42x^21

The gray image is a linear code over GF(3) with n=21, k=11 and d=4.
This code was found by Heurico 1.16 in 6.73 seconds.