The generator matrix

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

generates a code of length 89 over Z3[X]/(X^3) who´s minimum homogenous weight is 167.

Homogenous weight enumerator: w(x)=1x^0+270x^167+422x^168+726x^169+1530x^170+1514x^171+2562x^172+2838x^173+2852x^174+4164x^175+5088x^176+4100x^177+5448x^178+5592x^179+4628x^180+4626x^181+4698x^182+2296x^183+2166x^184+1404x^185+598x^186+522x^187+288x^188+180x^189+108x^190+78x^191+88x^192+54x^193+42x^194+42x^195+18x^196+42x^197+22x^198+12x^199+16x^201+6x^202+2x^204+4x^210+2x^213

The gray image is a linear code over GF(3) with n=801, k=10 and d=501.
This code was found by Heurico 1.16 in 14.3 seconds.