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

generates a code of length 81 over Z3[X]/(X^3) who´s minimum homogenous weight is 152.

Homogenous weight enumerator: w(x)=1x^0+348x^152+278x^153+18x^154+738x^155+616x^156+90x^157+1110x^158+1206x^159+1890x^160+1950x^161+2418x^162+3654x^163+1914x^164+1500x^165+180x^166+462x^167+192x^168+312x^170+146x^171+186x^173+96x^174+138x^176+78x^177+90x^179+8x^180+24x^182+20x^183+18x^185+2x^225

The gray image is a linear code over GF(3) with n=729, k=9 and d=456.
This code was found by Heurico 1.16 in 12 seconds.