The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  X  1  X  1  1  1  1  1  1  X  0  1  1  1
 0  X  0  0 2X 2X^2+X  X 2X^2+2X 2X 2X^2+X 2X^2  0 2X^2+X 2X^2+2X X^2 2X 2X^2+2X 2X^2+X 2X^2  0 2X^2+2X 2X^2+2X X^2+X X^2  X  X 2X X^2+2X 2X 2X^2+2X 2X^2+X 2X^2 X^2 X^2+X  X  0 2X 2X^2+X  X 2X^2+X 2X^2 2X X^2+X X^2 X^2+X 2X^2+X  X X^2+2X  X 2X^2 2X^2+2X  0 2X 2X^2+2X 2X^2 2X^2+X 2X 2X^2+2X 2X^2 X^2 2X^2+2X 2X^2+X 2X^2 2X^2+2X 2X^2+X 2X 2X X^2+X 2X^2+2X 2X^2 X^2+2X X^2 X^2+2X 2X^2 X^2 X^2+X 2X^2+X 2X^2
 0  0  X 2X  0 X^2+2X  X X^2+X X^2+2X 2X^2+2X  X 2X^2 X^2+X X^2+X 2X 2X^2 2X  0 X^2+2X X^2 X^2+X  0 X^2+2X 2X^2+X  0 X^2+X 2X^2+2X X^2+X X^2 X^2+2X 2X^2+2X 2X^2+X 2X^2 X^2+X 2X^2+2X X^2+2X 2X X^2 2X 2X^2+X 2X^2+2X 2X^2  0 X^2+X X^2  X 2X^2+X X^2+2X X^2 2X^2 2X^2 2X^2+2X X^2+2X 2X  0  0  X 2X^2+X X^2 X^2+2X 2X^2+X X^2  X X^2+X X^2 X^2  0 X^2+X X^2+2X  X X^2 2X^2+2X  0 2X^2+X  X X^2+X X^2 2X^2+X
 0  0  0 X^2  0  0  0 2X^2  0 X^2 2X^2 X^2 2X^2 X^2 2X^2  0  0 2X^2  0 X^2 2X^2  0 X^2  0 X^2 X^2 2X^2 2X^2 2X^2 X^2 2X^2  0  0 X^2 2X^2 2X^2 2X^2  0  0  0 X^2 X^2 2X^2 X^2 X^2  0 2X^2 X^2 X^2 2X^2 2X^2 X^2  0 2X^2 X^2 2X^2  0  0 2X^2  0 X^2  0 X^2 X^2 X^2 2X^2  0 2X^2 X^2 2X^2 X^2 X^2 X^2 2X^2 X^2  0 X^2 X^2
 0  0  0  0 X^2 2X^2 X^2  0 2X^2  0 2X^2 X^2  0  0  0  0  0 2X^2  0  0 X^2 2X^2 2X^2 2X^2 X^2 2X^2  0 2X^2 X^2 2X^2 2X^2 X^2 2X^2  0  0 X^2 X^2 X^2  0 2X^2 2X^2  0 X^2 2X^2 2X^2  0 X^2 X^2  0 2X^2 2X^2 X^2 X^2 2X^2 2X^2  0 X^2 2X^2 X^2 X^2 2X^2 2X^2  0 X^2  0  0  0 X^2 X^2  0 2X^2 X^2 X^2  0 2X^2 2X^2  0  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+192x^145+210x^146+92x^147+414x^148+450x^149+258x^150+510x^151+960x^152+732x^153+1914x^154+2544x^155+2864x^156+3192x^157+2334x^158+954x^159+390x^160+276x^161+90x^162+234x^163+234x^164+66x^165+228x^166+144x^167+30x^168+138x^169+78x^170+10x^171+54x^172+54x^173+18x^175+6x^176+6x^178+4x^180+2x^219

The gray image is a linear code over GF(3) with n=702, k=9 and d=435.
This code was found by Heurico 1.16 in 2.64 seconds.