The generator matrix
1 1 1 1 1 1 1 X X 1
0 X^2 2X^2 0 X^2 2X^2 0 X^2 2X^2 X^2
generates a code of length 10 over Z3[X]/(X^3) who´s minimum homogenous weight is 19.
Homogenous weight enumerator: w(x)=1x^0+12x^19+54x^20+4x^21+6x^22+4x^24
The gray image is a linear code over GF(3) with n=90, k=4 and d=57.
This code was found by Heurico 1.16 in 0.000179 seconds.