The generator matrix
1 1 1 1 1 1 1 1 1 X 1
0 X 2X X^2 2X^2+X X^2+2X 2X^2 X^2+X 2X^2+2X 2X^2+X 0
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+30x^20+2x^21+144x^22+60x^23+4x^24+2x^30
The gray image is a linear code over GF(3) with n=99, k=5 and d=60.
This code was found by Heurico 1.16 in 0.000316 seconds.