The generator matrix

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

generates a code of length 81 over Z3[X]/(X^2) who´s minimum homogenous weight is 143.

Homogenous weight enumerator: w(x)=1x^0+576x^143+512x^144+2442x^146+1652x^147+4860x^149+2846x^150+8124x^152+4582x^153+11556x^155+6422x^156+15054x^158+8072x^159+18174x^161+9314x^162+18042x^164+9234x^165+16152x^167+7342x^168+11778x^170+5012x^171+6960x^173+2488x^174+3102x^176+1160x^177+1026x^179+252x^180+204x^182+122x^183+36x^185+20x^186+12x^188+4x^189+4x^192+6x^198+4x^201

The gray image is a linear code over GF(3) with n=243, k=11 and d=143.
This code was found by Heurico 1.16 in 764 seconds.