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
 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  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
 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  0  X  X 2X  0  0 2X  X  0  0  X  X  X  0  X  0  X 2X 2X
 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  0  X

generates a code of length 59 over Z3[X]/(X^2) who´s minimum homogenous weight is 111.

Homogenous weight enumerator: w(x)=1x^0+22x^111+216x^113+66x^114+88x^117+44x^120+270x^122+2x^135+2x^138+6x^141+8x^144+4x^147

The gray image is a linear code over GF(3) with n=177, k=6 and d=111.
This code was found by Heurico 1.16 in 0.05 seconds.