The generator matrix

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

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+18x^143+166x^144+270x^145+174x^146+630x^147+1002x^148+516x^149+986x^150+1590x^151+840x^152+1560x^153+2184x^154+1440x^155+2192x^156+3210x^157+1758x^158+2600x^159+3906x^160+2022x^161+3234x^162+4080x^163+2070x^164+2780x^165+3846x^166+1890x^167+2444x^168+2970x^169+1302x^170+1654x^171+1884x^172+744x^173+784x^174+900x^175+258x^176+340x^177+336x^178+84x^179+116x^180+60x^181+68x^183+6x^184+6x^185+46x^186+40x^189+26x^192+10x^195+6x^198

The gray image is a linear code over GF(3) with n=243, k=10 and d=143.
This code was found by Heurico 1.16 in 71.8 seconds.