The generator matrix

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

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+270x^4+1140x^6+2160x^7+7290x^8+6640x^9+21060x^10+29160x^11+29238x^12+37800x^13+29160x^14+8832x^15+4320x^16+64x^18

The gray image is a linear code over GF(3) with n=18, k=11 and d=3.
This code was found by Heurico 1.16 in 5.8 seconds.