The generator matrix

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

generates a code of length 77 over Z3[X]/(X^3) who´s minimum homogenous weight is 145.

Homogenous weight enumerator: w(x)=1x^0+312x^145+630x^146+2072x^147+2652x^148+2928x^149+4138x^150+4944x^151+4860x^152+4842x^153+5328x^154+4170x^155+5214x^156+4860x^157+3282x^158+3330x^159+2238x^160+1452x^161+938x^162+486x^163+144x^164+82x^165+36x^166+18x^167+26x^168+18x^169+12x^171+12x^172+6x^173+12x^175+6x^179

The gray image is a linear code over GF(3) with n=693, k=10 and d=435.
This code was found by Heurico 1.16 in 9.05 seconds.