The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+12x^3+72x^4+60x^6+576x^7+160x^9+5616x^10+41064x^12+10080x^13+192x^15+1152x^16+64x^18

The gray image is a linear code over GF(3) with n=54, k=10 and d=9.
This code was found by Heurico 1.16 in 0.0975 seconds.