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

generates a code of length 81 over Z3[X]/(X^3) who´s minimum homogenous weight is 156.

Homogenous weight enumerator: w(x)=1x^0+1122x^156+1698x^157+1188x^158+2524x^159+2184x^160+1188x^161+1952x^162+1398x^163+774x^164+1482x^165+1068x^166+522x^167+964x^168+750x^169+198x^170+444x^171+186x^172+18x^173+6x^174+6x^175+4x^177+6x^180

The gray image is a linear code over GF(3) with n=729, k=9 and d=468.
This code was found by Heurico 1.16 in 2.23 seconds.