The generator matrix

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

generates a code of length 81 over Z3[X]/(X^2) who´s minimum homogenous weight is 148.

Homogenous weight enumerator: w(x)=1x^0+192x^148+294x^149+320x^150+534x^151+648x^152+614x^153+870x^154+954x^155+618x^156+978x^157+954x^158+684x^159+948x^160+1140x^161+666x^162+1110x^163+942x^164+670x^165+822x^166+876x^167+724x^168+798x^169+684x^170+404x^171+618x^172+456x^173+288x^174+264x^175+228x^176+88x^177+96x^178+102x^179+14x^180+48x^181+6x^182+8x^183+12x^184+6x^185+2x^186+2x^189

The gray image is a linear code over GF(3) with n=243, k=9 and d=148.
This code was found by Heurico 1.16 in 9.89 seconds.