The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X 1 1 X X X 1 X X X
0 X^2 2X^2 0 X^2 2X^2 0 X^2 2X^2 0 X^2 2X^2 0 X^2 2X^2 X^2 2X^2 0 X^2 0 X^2 2X^2 2X^2 0 X^2 0
generates a code of length 26 over Z3[X]/(X^3) who´s minimum homogenous weight is 51.
Homogenous weight enumerator: w(x)=1x^0+12x^51+54x^52+8x^54+6x^60
The gray image is a linear code over GF(3) with n=234, k=4 and d=153.
This code was found by Heurico 1.16 in 0.0029 seconds.