The generator matrix

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

generates a code of length 88 over Z3[X]/(X^2) who´s minimum homogenous weight is 172.

Homogenous weight enumerator: w(x)=1x^0+78x^172+132x^173+26x^174+150x^175+108x^176+26x^177+78x^178+60x^179+20x^180+6x^181+12x^182+2x^183+6x^185+6x^191+2x^192+4x^195+12x^199

The gray image is a linear code over GF(3) with n=264, k=6 and d=172.
This code was found by Heurico 1.13 in 0.156 seconds.