The generator matrix

 1  0  0  1  1  1  1  1  1 2X  1  1  1  0 2X  1  X  1  1  X  1  1  1  1  X  1  1  1  1  0  1  1  0  1  1  1  1  1  1  0 2X  1  1  1 2X 2X  0  0  1  X  X  1  1  1  1  1  X  1 2X  1  1  1  X  1  1 2X  1  1  1  1  1  X 2X  1  1  1  1  0  1  1  1  1  1 2X  1  1
 0  1  0 2X  1 2X+1  2  0 X+2  1 2X+2 2X+1 X+2  1  1  2  1 X+1  X  1 2X+2  0  1  2  0 2X+1 2X  X 2X  1 2X+2  2 2X X+1 2X+1  1  0  1  X  1  1 2X+2  X  2  1 2X  1  1 X+1  1  1 X+2  X X+1 2X X+1  X 2X+2  1  0 2X+2 2X  1 X+2 X+2  X  0  0  X  2 X+2  1  1 2X 2X 2X+1 2X+2  1  0 X+2 2X+2 X+2 2X  1 2X  0
 0  0  1 2X+1  1 2X 2X+2  2  X  1 X+2  2 X+1  2  X  X  1 2X+1 X+1 2X+2 2X  X  0  1  1 2X+2 X+2  0  1  X  0 2X+1  1 X+2  X X+1 2X+2 2X 2X+1 2X+2  0 X+1 2X  2  2  1 X+1 2X+1  1  X  0 X+2 X+2  2  2 2X+2  1 2X+1 X+2  1 2X+2  0 X+2  2  1  1 X+1 2X  X X+2 2X+2 2X 2X  X 2X  0  1 2X 2X+1 2X+1  2  0 X+1 2X+1 2X  0

generates a code of length 86 over Z3[X]/(X^2) who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+108x^168+42x^169+72x^170+172x^171+90x^172+72x^173+72x^174+18x^175+18x^176+18x^177+12x^178+8x^180+6x^183+4x^189+12x^192+4x^198

The gray image is a linear code over GF(3) with n=258, k=6 and d=168.
This code was found by Heurico 1.16 in 0.105 seconds.