The generator matrix

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

generates a code of length 78 over Z3[X]/(X^3) who´s minimum homogenous weight is 145.

Homogenous weight enumerator: w(x)=1x^0+198x^145+600x^146+310x^147+1050x^148+1986x^149+1902x^150+2574x^151+3744x^152+4094x^153+3630x^154+5364x^155+6418x^156+5298x^157+5394x^158+5374x^159+3348x^160+3492x^161+1392x^162+930x^163+978x^164+136x^165+276x^166+162x^167+8x^168+126x^169+96x^170+26x^171+48x^172+24x^173+10x^174+18x^175+18x^176+6x^177+12x^179+4x^180+2x^183

The gray image is a linear code over GF(3) with n=702, k=10 and d=435.
This code was found by Heurico 1.16 in 12.4 seconds.