The generator matrix

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

generates a code of length 81 over Z3[X]/(X^3) who´s minimum homogenous weight is 150.

Homogenous weight enumerator: w(x)=1x^0+1062x^150+2172x^151+4032x^152+7482x^153+10200x^154+13980x^155+19442x^156+22938x^157+27504x^158+37240x^159+39672x^160+45276x^161+51748x^162+47124x^163+45204x^164+44584x^165+35760x^166+26982x^167+21320x^168+12636x^169+7176x^170+4354x^171+1860x^172+798x^173+496x^174+138x^175+60x^176+72x^177+24x^178+36x^179+24x^180+12x^182+14x^183+6x^184+12x^185

The gray image is a linear code over GF(3) with n=729, k=12 and d=450.
This code was found by Heurico 1.16 in 664 seconds.