The generator matrix

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

generates a code of length 82 over Z3[X]/(X^3) who´s minimum homogenous weight is 152.

Homogenous weight enumerator: w(x)=1x^0+1020x^152+1962x^153+4758x^154+8082x^155+9968x^156+12858x^157+20742x^158+22748x^159+27018x^160+38220x^161+39482x^162+41214x^163+55200x^164+47200x^165+42900x^166+47166x^167+35412x^168+25254x^169+22008x^170+11964x^171+7620x^172+4710x^173+1920x^174+1032x^175+576x^176+130x^177+84x^178+60x^179+36x^180+48x^181+12x^182+18x^184+6x^185+6x^186+6x^187

The gray image is a linear code over GF(3) with n=738, k=12 and d=456.
This code was found by Heurico 1.16 in 673 seconds.