The generator matrix

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

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+432x^152+814x^153+972x^154+1626x^155+2282x^156+3096x^157+2670x^158+4500x^159+5202x^160+4050x^161+5656x^162+6660x^163+4008x^164+5154x^165+4950x^166+2130x^167+2196x^168+900x^169+600x^170+322x^171+90x^172+282x^173+114x^174+126x^176+48x^177+66x^179+36x^180+42x^182+10x^183+6x^185+6x^186+2x^189

The gray image is a linear code over GF(3) with n=729, k=10 and d=456.
This code was found by Heurico 1.16 in 16.9 seconds.