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.