The generator matrix

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

generates a code of length 7 over Z3[X]/(X^3) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+54x^11+514x^12+540x^14+1020x^15+54x^17+2x^18+2x^21

The gray image is a linear code over GF(3) with n=63, k=7 and d=33.
This code was found by Heurico 1.16 in 0.00103 seconds.