The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
0 X^2 0 X^2 0 X^2 2X^2 2X^2 2X^2 0 0 X^2 X^2 0 X^2 2X^2 2X^2 2X^2 0
0 0 X^2 2X^2 2X^2 X^2 0 X^2 2X^2 0 X^2 2X^2 X^2 2X^2 0 0 X^2 2X^2 0
generates a code of length 19 over Z3[X]/(X^3) who´s minimum homogenous weight is 36.
Homogenous weight enumerator: w(x)=1x^0+8x^36+216x^38+16x^39+2x^57
The gray image is a linear code over GF(3) with n=171, k=5 and d=108.
This code was found by Heurico 1.16 in 0.0012 seconds.