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

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+348x^146+258x^147+786x^149+450x^150+738x^152+354x^153+636x^155+318x^156+624x^158+228x^159+456x^161+214x^162+264x^164+162x^165+276x^167+120x^168+132x^170+50x^171+84x^173+18x^174+24x^176+12x^177+6x^179+2x^180

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 0.907 seconds.