The generator matrix

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

generates a code of length 82 over Z3[X]/(X^3) who´s minimum homogenous weight is 153.

Homogenous weight enumerator: w(x)=1x^0+752x^153+966x^154+2070x^155+4196x^156+5184x^157+6366x^158+8430x^159+9456x^160+11454x^161+14328x^162+13662x^163+16002x^164+18442x^165+14994x^166+13338x^167+13352x^168+8166x^169+6138x^170+4518x^171+2382x^172+1308x^173+696x^174+372x^175+108x^176+106x^177+126x^178+48x^179+48x^180+72x^181+24x^182+12x^183+24x^184+6x^185

The gray image is a linear code over GF(3) with n=738, k=11 and d=459.
This code was found by Heurico 1.16 in 88.5 seconds.