The generator matrix

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

generates a code of length 89 over Z3[X]/(X^2) who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+600x^168+1126x^171+1218x^174+930x^177+840x^180+558x^183+456x^186+374x^189+186x^192+156x^195+98x^198+18x^201

The gray image is a linear code over GF(3) with n=267, k=8 and d=168.
This code was found by Heurico 1.16 in 1.33 seconds.