The generator matrix
1 1 1 1 1 X
0 X 2X 0 X^2 2X^2+X
0 0 X^2 X^2 2X^2 2X^2
generates a code of length 6 over Z3[X]/(X^3) who´s minimum homogenous weight is 9.
Homogenous weight enumerator: w(x)=1x^0+26x^9+108x^10+348x^12+216x^13+30x^15
The gray image is a linear code over GF(3) with n=54, k=6 and d=27.
This code was found by Heurico 1.16 in 0.00028 seconds.