The generator matrix

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

generates a code of length 11 over Z3[X]/(X^3) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+168x^20+62x^21+126x^22+336x^23+32x^24+4x^27

The gray image is a linear code over GF(3) with n=99, k=6 and d=60.
This code was found by Heurico 1.16 in 0.000441 seconds.