The generator matrix

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

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+438x^151+810x^152+2448x^153+4356x^154+4218x^155+7044x^156+8400x^157+9264x^158+12734x^159+13932x^160+13722x^161+16894x^162+16782x^163+13698x^164+15332x^165+12984x^166+7812x^167+6906x^168+4410x^169+2028x^170+1370x^171+690x^172+288x^173+112x^174+156x^175+102x^176+64x^177+48x^178+36x^179+26x^180+6x^181+12x^182+6x^183+6x^184+12x^185

The gray image is a linear code over GF(3) with n=729, k=11 and d=453.
This code was found by Heurico 1.16 in 87.7 seconds.