The generator matrix

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

generates a code of length 78 over Z3[X]/(X^2) who´s minimum homogenous weight is 146.

Homogenous weight enumerator: w(x)=1x^0+312x^146+332x^147+822x^149+318x^150+750x^152+388x^153+660x^155+348x^156+582x^158+252x^159+420x^161+180x^162+318x^164+158x^165+282x^167+120x^168+108x^170+52x^171+96x^173+24x^174+24x^176+12x^177+2x^183

The gray image is a linear code over GF(3) with n=234, k=8 and d=146.
This code was found by Heurico 1.16 in 0.822 seconds.