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.