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  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  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  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  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  0

generates a code of length 88 over Z3[X]/(X^2) who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+20x^168+30x^171+50x^174+486x^176+70x^177+50x^180+20x^183+2x^264

The gray image is a linear code over GF(3) with n=264, k=6 and d=168.
This code was found by Heurico 1.16 in 0.109 seconds.