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 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 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 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 X 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 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 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 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 X 2X 2X 2X
generates a code of length 86 over Z3[X]/(X^2) who´s minimum homogenous weight is 165.
Homogenous weight enumerator: w(x)=1x^0+10x^165+40x^168+80x^171+486x^172+80x^174+30x^177+2x^258
The gray image is a linear code over GF(3) with n=258, k=6 and d=165.
This code was found by Heurico 1.16 in 0.102 seconds.