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 1 1 1 1 1 1 1 1 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 2X 2X 0 2X X X 0 0 X X 2X 2X 0 X 2X 0 X 2X 2X 0 0 2X 0 X 2X 2X X 2X X 0 X 0 X 2X 2X 2X 0 0 X X 0 X 2X 2X 2X 0 0 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 2X 0 2X X X 0 2X 2X 2X 0 X 0 2X 0 2X 2X 2X 0 2X 0 0 2X 2X 0 0 2X 2X 0 X 0 2X 2X 0 0 X 2X X X X X X X X X X 0 0 0
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 2X 2X X 0 X 2X 2X 0 0 2X 0 2X 0 X 0 2X 0 2X 2X 0 X X X X X X X 2X X 0 X 0 2X 2X X 0 0 0 0
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 X 0 0 2X 2X 0 2X X X X 2X 0 0 2X 2X 0 X X X X X X X X X X X X X 0 0 X 0 2X 2X 2X 0 0 0
generates a code of length 84 over Z3[X]/(X^2) who´s minimum homogenous weight is 162.
Homogenous weight enumerator: w(x)=1x^0+80x^162+486x^168+160x^171+2x^252
The gray image is a linear code over GF(3) with n=252, k=6 and d=162.
This code was found by Heurico 1.16 in 0.0948 seconds.