The generator matrix

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

generates a code of length 6 over Z3[X]/(X^2) who´s minimum homogenous weight is 3.

Homogenous weight enumerator: w(x)=1x^0+12x^3+108x^4+492x^6+864x^7+1458x^8+2752x^9+8424x^10+5832x^11+12714x^12+15120x^13+5832x^14+3648x^15+1728x^16+64x^18

The gray image is a linear code over GF(3) with n=18, k=10 and d=3.
This code was found by Heurico 1.16 in 0.203 seconds.