The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 X 1 1 1 X X 1 X^2 X^2 X 0 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 0 2X^2 X^2 2X^2 0 X^2 2X^2 0 X^2 2X^2 0 X^2 X^2
generates a code of length 29 over Z3[X]/(X^3) who´s minimum homogenous weight is 58.
Homogenous weight enumerator: w(x)=1x^0+66x^58+4x^60+6x^61+4x^66
The gray image is a linear code over GF(3) with n=261, k=4 and d=174.
This code was found by Heurico 1.16 in 0.00447 seconds.