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

generates a code of length 63 over Z3[X]/(X^2) who´s minimum homogenous weight is 120.

Homogenous weight enumerator: w(x)=1x^0+60x^120+56x^123+162x^124+48x^126+324x^127+24x^129+24x^132+14x^135+6x^138+8x^141+2x^186

The gray image is a linear code over GF(3) with n=189, k=6 and d=120.
This code was found by Heurico 1.16 in 0.0679 seconds.