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

generates a code of length 88 over Z3[X]/(X^3) who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+268x^168+108x^169+126x^170+238x^171+270x^172+396x^173+664x^174+648x^175+810x^176+1100x^177+864x^178+576x^179+102x^180+36x^182+78x^183+122x^186+64x^189+54x^190+30x^192+4x^204+2x^246

The gray image is a linear code over GF(3) with n=792, k=8 and d=504.
This code was found by Heurico 1.16 in 0.76 seconds.