The generator matrix
1 1 1 1 1 1 1
0 X 2X 0 2X^2+X X^2 2X^2+X
0 0 X^2 X^2 2X^2 2X^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+36x^11+28x^12+576x^14+48x^15+36x^17+2x^18+2x^21
The gray image is a linear code over GF(3) with n=63, k=6 and d=33.
This code was found by Heurico 1.16 in 0.000359 seconds.