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

generates a code of length 79 over Z3[X]/(X^3) who´s minimum homogenous weight is 152.

Homogenous weight enumerator: w(x)=1x^0+1212x^152+1284x^153+1530x^154+2598x^155+1938x^156+1152x^157+2136x^158+1302x^159+990x^160+1464x^161+1050x^162+576x^163+966x^164+566x^165+252x^166+522x^167+90x^168+36x^169+6x^170+2x^171+4x^174+6x^176

The gray image is a linear code over GF(3) with n=711, k=9 and d=456.
This code was found by Heurico 1.16 in 1.17 seconds.