The generator matrix

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

generates a code of length 77 over Z3[X]/(X^3) who´s minimum homogenous weight is 146.

Homogenous weight enumerator: w(x)=1x^0+198x^146+498x^147+822x^148+1464x^149+1278x^150+1308x^151+1818x^152+1604x^153+1650x^154+2340x^155+1570x^156+1374x^157+1386x^158+764x^159+546x^160+444x^161+286x^162+72x^163+84x^164+28x^165+36x^166+6x^167+16x^168+18x^169+24x^170+14x^171+6x^172+6x^173+14x^174+6x^176+2x^183

The gray image is a linear code over GF(3) with n=693, k=9 and d=438.
This code was found by Heurico 1.16 in 1.64 seconds.