The generator matrix

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

generates a code of length 89 over Z3[X]/(X^3) who´s minimum homogenous weight is 169.

Homogenous weight enumerator: w(x)=1x^0+582x^169+846x^170+2256x^171+2868x^172+3006x^173+4598x^174+4356x^175+4356x^176+5556x^177+4404x^178+4140x^179+5416x^180+3204x^181+3474x^182+3266x^183+2406x^184+1422x^185+1350x^186+888x^187+252x^188+114x^189+156x^190+20x^192+54x^193+6x^195+18x^196+16x^198+6x^202+12x^205

The gray image is a linear code over GF(3) with n=801, k=10 and d=507.
This code was found by Heurico 1.16 in 10.7 seconds.