The generator matrix

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

generates a code of length 81 over Z3[X]/(X^2) who´s minimum homogenous weight is 154.

Homogenous weight enumerator: w(x)=1x^0+114x^154+264x^155+64x^156+300x^157+126x^158+82x^159+90x^160+150x^161+22x^162+144x^163+198x^164+26x^165+132x^166+60x^167+16x^168+66x^169+66x^170+2x^171+66x^172+78x^173+4x^174+54x^175+30x^176+6x^177+6x^178+2x^180+12x^183+2x^186+2x^192+2x^195

The gray image is a linear code over GF(3) with n=243, k=7 and d=154.
This code was found by Heurico 1.16 in 28 seconds.