The generator matrix

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

generates a code of length 96 over Z3[X]/(X^2) who´s minimum homogenous weight is 171.

Homogenous weight enumerator: w(x)=1x^0+134x^171+390x^172+354x^173+1000x^174+1728x^175+1092x^176+1944x^177+2958x^178+1758x^179+3154x^180+5046x^181+2844x^182+4692x^183+7032x^184+3780x^185+6236x^186+9072x^187+5058x^188+7622x^189+10344x^190+5340x^191+8328x^192+11316x^193+5508x^194+8360x^195+10602x^196+5232x^197+6838x^198+8694x^199+3732x^200+5092x^201+6120x^202+2562x^203+3260x^204+3048x^205+1386x^206+1566x^207+1602x^208+522x^209+574x^210+630x^211+180x^212+174x^213+132x^214+12x^215+36x^216+6x^217+6x^218+22x^219+12x^220+6x^222+6x^225+2x^228+2x^234

The gray image is a linear code over GF(3) with n=288, k=11 and d=171.
This code was found by Heurico 1.16 in 817 seconds.