The generator matrix

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

generates a code of length 97 over Z3[X]/(X^3) who´s minimum homogenous weight is 183.

Homogenous weight enumerator: w(x)=1x^0+268x^183+402x^184+888x^185+1358x^186+2154x^187+2310x^188+3152x^189+3072x^190+3498x^191+4046x^192+5520x^193+5082x^194+5164x^195+4806x^196+4536x^197+3806x^198+3294x^199+2034x^200+1192x^201+894x^202+396x^203+324x^204+150x^205+132x^206+194x^207+66x^208+54x^209+92x^210+18x^211+6x^212+42x^213+18x^214+16x^216+12x^217+12x^218+18x^219+6x^220+6x^222+6x^224+4x^225

The gray image is a linear code over GF(3) with n=873, k=10 and d=549.
This code was found by Heurico 1.16 in 31.9 seconds.