The generator matrix

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

generates a code of length 89 over Z3[X]/(X^3) who´s minimum homogenous weight is 165.

Homogenous weight enumerator: w(x)=1x^0+404x^165+816x^166+3132x^167+5136x^168+8244x^169+11202x^170+15274x^171+18588x^172+24684x^173+29336x^174+34962x^175+37716x^176+43944x^177+46524x^178+45534x^179+46268x^180+41490x^181+35322x^182+27734x^183+21066x^184+14706x^185+9352x^186+4488x^187+2736x^188+1470x^189+624x^190+324x^191+96x^192+72x^193+48x^194+38x^195+18x^196+36x^197+20x^198+12x^199+6x^200+18x^201

The gray image is a linear code over GF(3) with n=801, k=12 and d=495.
This code was found by Heurico 1.16 in 739 seconds.