The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  1  1  0  1  1  X  1  1  X 2X^2  1  1  1  1
 0  X  0  0 2X 2X^2+X  X 2X^2+2X 2X X^2 2X^2 2X^2 2X 2X^2+2X 2X^2+2X  X X^2+X X^2+X X^2 2X 2X^2+2X  0 X^2+X 2X 2X^2+X 2X^2 2X^2+X 2X^2+X X^2+2X  X 2X X^2 2X X^2+X X^2 2X^2 X^2 X^2 X^2  X 2X X^2+2X 2X^2+2X 2X^2+X 2X 2X^2+2X X^2 X^2+2X  X X^2 X^2+X X^2 2X^2+2X 2X^2 2X^2+X 2X^2 2X^2+X  X 2X^2+X  X X^2 2X^2 2X^2 2X^2 2X^2+2X 2X^2+X  X 2X^2+2X  0  0 X^2+X 2X^2 2X^2+X X^2+X  0 2X  X 2X^2+X 2X^2+X X^2+2X 2X
 0  0  X 2X  0 X^2+2X  X X^2+X 2X 2X^2 2X^2+X 2X 2X^2 2X^2+X 2X  X X^2+2X  0 X^2+2X 2X^2+X X^2+2X X^2 2X^2+2X X^2  0 2X^2+X  X 2X^2+2X  X X^2+X 2X^2  0 2X^2 2X^2 2X^2+2X X^2+2X  0 X^2+X 2X^2+2X 2X X^2+2X X^2 2X^2+X X^2 X^2+2X 2X^2+2X  X  0  X X^2 2X^2+X 2X^2 X^2+2X X^2+X 2X 2X 2X^2+X X^2 2X^2+X  X  X X^2+X X^2+X 2X^2+X X^2+X X^2+2X 2X^2 X^2+X 2X^2+2X  X X^2 2X^2+2X 2X^2  0 2X^2+X 2X  X 2X  0  X X^2+2X
 0  0  0 X^2  0  0  0 2X^2 X^2 2X^2 2X^2 2X^2 X^2 X^2  0 X^2 2X^2 X^2  0  0 2X^2 X^2 X^2 2X^2 2X^2 X^2 2X^2 X^2 2X^2 X^2  0 2X^2  0  0  0  0 2X^2  0 2X^2  0 2X^2 X^2 2X^2 2X^2 2X^2 X^2 2X^2 X^2 X^2  0 2X^2  0  0 X^2  0 X^2  0 2X^2  0 2X^2 X^2 2X^2 X^2  0 X^2 2X^2 X^2  0 X^2  0 2X^2  0 X^2  0 2X^2 2X^2 2X^2 X^2 X^2 2X^2 X^2
 0  0  0  0 X^2 2X^2 X^2  0 2X^2  0 X^2 2X^2  0 X^2  0  0  0 2X^2 X^2 2X^2 X^2 2X^2 X^2 X^2  0 X^2  0 2X^2 2X^2 X^2  0 2X^2 2X^2 2X^2 2X^2  0 X^2 X^2 X^2  0 2X^2 X^2 X^2 2X^2  0 X^2  0 2X^2 2X^2 2X^2 2X^2 X^2 2X^2  0 X^2 2X^2 2X^2 X^2  0 X^2 2X^2  0 X^2  0  0 2X^2 X^2 X^2 X^2 2X^2 X^2 2X^2 X^2 X^2 X^2 2X^2 X^2  0 2X^2 X^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+138x^151+330x^152+44x^153+480x^154+396x^155+190x^156+522x^157+1200x^158+1274x^159+924x^160+2970x^161+3434x^162+1326x^163+2976x^164+1528x^165+288x^166+306x^167+50x^168+264x^169+240x^170+14x^171+174x^172+138x^173+8x^174+174x^175+114x^176+6x^177+42x^178+78x^179+6x^180+36x^181+2x^183+6x^184+2x^186+2x^225

The gray image is a linear code over GF(3) with n=729, k=9 and d=453.
This code was found by Heurico 1.16 in 2.78 seconds.