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.