The generator matrix

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

generates a code of length 78 over Z3[X]/(X^2) who´s minimum homogenous weight is 145.

Homogenous weight enumerator: w(x)=1x^0+108x^145+306x^146+80x^147+474x^148+462x^149+148x^150+522x^151+486x^152+110x^153+378x^154+408x^155+102x^156+390x^157+372x^158+102x^159+414x^160+306x^161+76x^162+258x^163+240x^164+48x^165+210x^166+144x^167+34x^168+90x^169+144x^170+20x^171+60x^172+36x^173+4x^174+6x^175+12x^176+2x^177+6x^181+2x^195

The gray image is a linear code over GF(3) with n=234, k=8 and d=145.
This code was found by Heurico 1.16 in 0.821 seconds.