The generator matrix

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

generates a code of length 60 over Z3[X]/(X^3) who´s minimum homogenous weight is 117.

Homogenous weight enumerator: w(x)=1x^0+138x^117+162x^118+18x^120+324x^121+18x^123+64x^126+2x^135+2x^153

The gray image is a linear code over GF(3) with n=540, k=6 and d=351.
This code was found by Heurico 1.16 in 0.247 seconds.