The generator matrix

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

generates a code of length 81 over Z3[X]/(X^3) who´s minimum homogenous weight is 151.

Homogenous weight enumerator: w(x)=1x^0+234x^151+432x^152+308x^153+1326x^154+1986x^155+1040x^156+3258x^157+4266x^158+2334x^159+4836x^160+7416x^161+3264x^162+5946x^163+7350x^164+2940x^165+4452x^166+3960x^167+846x^168+1332x^169+474x^170+132x^171+234x^172+240x^173+28x^174+150x^175+102x^176+24x^177+60x^178+12x^179+10x^180+36x^181+2x^183+6x^184+6x^185+2x^189+4x^192

The gray image is a linear code over GF(3) with n=729, k=10 and d=453.
This code was found by Heurico 1.16 in 25.4 seconds.