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

generates a code of length 60 over Z3[X]/(X^2) who´s minimum homogenous weight is 117.

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

The gray image is a linear code over GF(3) with n=180, k=5 and d=117.
This code was found by Heurico 1.16 in 0.76 seconds.