The generator matrix

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

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+306x^8+60x^9+2322x^10+1224x^11+9840x^12+4644x^13+1224x^14+60x^15+2x^18

The gray image is a linear code over GF(3) with n=54, k=9 and d=24.
This code was found by Heurico 1.16 in 0.0264 seconds.