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.