The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  0  X  X X^2  X  X
 0  X 2X X^2 2X^2+X X^2+2X 2X^2 X^2+X 2X^2+2X  0 2X^2+X 2X X^2 X^2+X X^2+2X 2X^2  X 2X^2+2X 2X^2+X 2X  X X^2+X X^2+2X  X  X 2X^2+2X

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+48x^51+162x^52+26x^54+6x^60

The gray image is a linear code over GF(3) with n=234, k=5 and d=153.
This code was found by Heurico 1.16 in 0.0031 seconds.