The generator matrix

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

generates a code of length 84 over Z3[X]/(X^3) who´s minimum homogenous weight is 162.

Homogenous weight enumerator: w(x)=1x^0+1148x^162+1620x^163+1992x^164+2058x^165+1572x^166+1206x^167+2050x^168+1632x^169+966x^170+1274x^171+912x^172+774x^173+888x^174+516x^175+372x^176+396x^177+216x^178+36x^179+40x^180+12x^184+2x^186

The gray image is a linear code over GF(3) with n=756, k=9 and d=486.
This code was found by Heurico 1.16 in 86.9 seconds.