The generator matrix

 1  0  0  0  1  1  1
 0  1  0  0  1  0 2X+1
 0  0  1  0  2  1 2X+1
 0  0  0  1  2  2 2X+1
 0  0  0  0 2X  0  X
 0  0  0  0  0 2X 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+132x^6+810x^8+790x^9+1458x^10+4860x^11+6258x^12+5832x^13+14094x^14+10866x^15+5832x^16+6480x^17+1594x^18+42x^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 0.406 seconds.