The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+202x^6+48x^7+1998x^8+1212x^9+21510x^10+7992x^11+91500x^12+43020x^13+7992x^14+1604x^15+60x^16+8x^18

The gray image is a linear code over GF(3) with n=54, k=11 and d=18.
This code was found by Heurico 1.16 in 0.983 seconds.