The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X X X 1 1 X X X 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 X^2 X^2 0 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 X^2 2X^2 X^2 2X^2 0 0 2X^2 0 2X^2 X^2 X^2
generates a code of length 29 over Z3[X]/(X^3) who´s minimum homogenous weight is 57.
Homogenous weight enumerator: w(x)=1x^0+54x^57+162x^58+12x^60+8x^63+6x^66
The gray image is a linear code over GF(3) with n=261, k=5 and d=171.
This code was found by Heurico 1.16 in 0.00467 seconds.