The generator matrix

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

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+128x^6+102x^7+504x^8+852x^9+2526x^10+3024x^11+6284x^12+9468x^13+9936x^14+10618x^15+9528x^16+4032x^17+1784x^18+246x^19+16x^21

The gray image is a linear code over GF(3) with n=21, k=10 and d=6.
This code was found by Heurico 1.16 in 1.12 seconds.