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 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 2X 2X 0 2X X X 0 0 0 X X X 0 X 0 X 0 X 0 2X X 0 2X X 2X 0 X 0 2X X 2X 2X 2X 2X 0 X 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 2X 0 2X X X 0 2X 2X 2X X 2X 0 2X X 0 2X 0 X X 0 0 X 2X 2X 0 2X X 0 0 0 X X X 0 X 2X 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 0 2X 0 0 0 X X 2X 2X 0 0 X 2X 0 2X X 2X 2X X 2X 0 X 2X 0 2X 2X 0 X 0 X X
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 2X 0 X X X X 0 2X 0 X 2X 2X 0 0 2X 2X 0 X X X X 0 X X 2X X X 0 2X 2X 0 2X 0 X X X
generates a code of length 73 over Z3[X]/(X^2) who´s minimum homogenous weight is 141.
Homogenous weight enumerator: w(x)=1x^0+60x^141+222x^144+378x^147+42x^150+18x^153+6x^159+2x^216
The gray image is a linear code over GF(3) with n=219, k=6 and d=141.
This code was found by Heurico 1.16 in 0.0893 seconds.