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

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+130x^168+96x^169+180x^170+406x^171+396x^172+348x^173+478x^174+1170x^175+492x^176+726x^177+1110x^178+324x^179+214x^180+60x^181+18x^182+78x^183+48x^184+60x^185+60x^186+12x^187+18x^188+56x^189+12x^190+12x^191+26x^192+6x^193+6x^194+8x^195+6x^196+2x^198+2x^243

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 0.688 seconds.