The generator matrix

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

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+96x^6+18x^7+810x^8+562x^9+5508x^10+3240x^11+33822x^12+10962x^13+3240x^14+750x^15+36x^16+4x^18

The gray image is a linear code over GF(3) with n=54, k=10 and d=18.
This code was found by Heurico 1.16 in 0.115 seconds.