The generator matrix

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

generates a code of length 81 over Z3[X]/(X^3) who´s minimum homogenous weight is 147.

Homogenous weight enumerator: w(x)=1x^0+40x^147+114x^149+160x^150+90x^151+456x^152+810x^153+1008x^154+1176x^155+1950x^156+2844x^157+2022x^158+5330x^159+5094x^160+3186x^161+7066x^162+7254x^163+3090x^164+5890x^165+4284x^166+2100x^167+2352x^168+1296x^169+672x^170+266x^171+270x^173+86x^174+30x^176+22x^177+6x^179+22x^180+14x^183+18x^186+6x^189+10x^192+2x^195+6x^198+2x^201+4x^207

The gray image is a linear code over GF(3) with n=729, k=10 and d=441.
This code was found by Heurico 1.16 in 13.5 seconds.