The generator matrix

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

generates a code of length 78 over Z3[X]/(X^3) who´s minimum homogenous weight is 146.

Homogenous weight enumerator: w(x)=1x^0+462x^146+462x^147+522x^148+1956x^149+2778x^150+2196x^151+3402x^152+5132x^153+3312x^154+5250x^155+6846x^156+4770x^157+5304x^158+6324x^159+3150x^160+2868x^161+2068x^162+630x^163+636x^164+260x^165+276x^167+108x^168+144x^170+38x^171+78x^173+26x^174+24x^176+6x^177+12x^179+6x^180+2x^183

The gray image is a linear code over GF(3) with n=702, k=10 and d=438.
This code was found by Heurico 1.16 in 28.5 seconds.