The generator matrix

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

generates a code of length 5 over Z3[X]/(X^3) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+108x^8+14x^9+378x^10+216x^11+12x^12

The gray image is a linear code over GF(3) with n=45, k=6 and d=24.
This code was found by Heurico 1.16 in 0.000121 seconds.