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

generates a code of length 60 over Z3[X]/(X^2) who´s minimum homogenous weight is 114.

Homogenous weight enumerator: w(x)=1x^0+52x^114+216x^115+58x^117+84x^120+26x^123+270x^124+2x^135+8x^141+2x^144+6x^147+4x^150

The gray image is a linear code over GF(3) with n=180, k=6 and d=114.
This code was found by Heurico 1.16 in 0.0523 seconds.