The generator matrix

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

generates a code of length 6 over Z3[X]/(X^3) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+72x^8+60x^9+810x^10+288x^11+3360x^12+1620x^13+288x^14+60x^15+2x^18

The gray image is a linear code over GF(3) with n=54, k=8 and d=24.
This code was found by Heurico 1.16 in 0.004 seconds.