The generator matrix

 1  0  1  1  1  1
 0  1  1  0 2X+1  0
 0  0 2X 2X^2+X  X 2X
 0  0  0 2X^2  0 X^2
 0  0  0  0 X^2 2X^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+138x^6+486x^8+688x^9+6804x^10+1944x^11+32490x^12+13608x^13+1944x^14+924x^15+22x^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 0.148 seconds.