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  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  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  X
 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  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  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  X

generates a code of length 87 over Z3[X]/(X^2) who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+30x^168+40x^171+576x^174+60x^177+20x^180+2x^261

The gray image is a linear code over GF(3) with n=261, k=6 and d=168.
This code was found by Heurico 1.16 in 0.138 seconds.