The generator matrix

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

generates a code of length 89 over Z3[X]/(X^3) who´s minimum homogenous weight is 170.

Homogenous weight enumerator: w(x)=1x^0+348x^170+510x^171+774x^172+1536x^173+1064x^174+1368x^175+2232x^176+1356x^177+1692x^178+2454x^179+1028x^180+1116x^181+1368x^182+842x^183+846x^184+624x^185+240x^186+36x^187+78x^188+10x^189+36x^191+8x^192+36x^194+6x^195+12x^197+20x^198+12x^200+12x^201+6x^203+6x^206+6x^207

The gray image is a linear code over GF(3) with n=801, k=9 and d=510.
This code was found by Heurico 1.16 in 2.09 seconds.