The generator matrix

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

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+42x^171+42x^172+144x^173+360x^174+276x^175+528x^176+720x^177+468x^178+1332x^179+1240x^180+720x^181+1878x^182+1480x^183+1314x^184+2514x^185+2016x^186+1560x^187+3288x^188+2586x^189+1710x^190+3852x^191+2716x^192+1896x^193+3696x^194+2652x^195+1872x^196+3630x^197+2208x^198+1254x^199+2610x^200+1656x^201+1206x^202+1584x^203+1056x^204+522x^205+822x^206+464x^207+216x^208+264x^209+220x^210+60x^211+102x^212+118x^213+6x^214+50x^216+40x^219+16x^222+24x^225+8x^228+10x^231

The gray image is a linear code over GF(3) with n=288, k=10 and d=171.
This code was found by Heurico 1.16 in 80.1 seconds.