The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 X 1 1 1 X 1 1 1 0 1 1 1 1 1 0 1 1 X 1 1 2X 1 1 0 1 1 1 1 2X 1 1 1 1 1 X 1 0 1 2X 1 1 1 1 1 1 X 1 1 2X 0 1 1 X 1 1 0 1 1 1 1 2X 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 1 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 X+1 X+2 1 1 X 2 2X+1 1 2 2X+1 0 1 2X+1 2 0 X+1 2X+2 1 0 2X+1 1 2 2X 1 X+1 2X 1 X+2 X+1 2X+1 X+2 1 2 X 2X X+2 1 1 X+2 1 X 1 0 2X X 2 X+1 0 1 X X+2 1 1 0 2X 1 1 X+2 1 1 2X+2 0 2 1 X 2 X+2 2X+2 2X+1 2X 1 2 X+1 X X 2 2X+1 1 X 2 0
0 0 2X 0 0 0 0 0 0 0 0 0 0 X 0 X 2X 0 X 2X X X X 0 2X 0 2X X 0 X 0 X 2X 2X 2X X 2X 0 X 0 X X 2X 0 2X X X 2X 0 2X 2X X 2X X X X 0 2X 2X 0 X X 2X 2X X 2X 0 0 X X X 0 2X X 2X 2X 2X 2X 2X 0 2X 2X 2X X X X X X 2X 0 X X X 0
0 0 0 X 0 0 0 0 0 0 0 2X 0 0 2X X 2X 0 2X X 0 X X 2X X 2X X 0 X 2X X 0 2X 0 X X X X 0 2X 0 2X 2X X 0 X X X 2X X 2X 0 0 0 0 X X 0 2X X 2X X 2X 2X 0 0 2X X X 0 X 0 0 X 0 X 2X 0 2X 0 X X X 2X 2X 2X X 0 2X 0 X 2X 0 0
0 0 0 0 X 0 0 0 X 2X 2X 0 X 2X 2X 0 0 2X X X 0 2X 0 X X 2X 0 X X 2X 2X 0 0 X 2X 0 X 0 X 0 0 0 X X 0 X 2X X 0 0 2X 0 X 0 X 0 X 2X X X X 2X X X 0 2X 0 2X X 2X 2X 2X 0 X 2X 0 2X 2X 2X X X X 2X 0 X 0 2X 2X X 0 0 X X X
0 0 0 0 0 2X 0 X 2X 2X 2X 2X 0 X 2X 2X 2X X X 0 0 X X 0 2X X 0 2X X 2X 2X X X X 0 X 0 0 0 X X 2X X X 0 2X X 0 0 0 0 X 0 0 X X 0 0 2X 0 0 0 X 2X 2X 2X 2X 0 X 2X 0 X X X 0 X 2X 2X 2X 2X 2X 0 X 2X 0 X 2X 2X X 0 2X 2X X 2X
0 0 0 0 0 0 X 2X 2X 2X 0 2X 2X 2X X 2X 0 2X 2X 0 2X 0 0 0 2X 0 0 X 0 X X X 0 X 2X X X 2X X X 0 0 X 2X 2X X X X 0 2X X 2X 0 2X X 2X 0 0 X X 0 2X 0 2X X X 0 X 0 X 2X X 2X X 2X 0 X 0 2X 2X 2X X 0 2X X 2X 0 X 0 2X 0 X 0 X
generates a code of length 94 over Z3[X]/(X^2) who´s minimum homogenous weight is 168.
Homogenous weight enumerator: w(x)=1x^0+58x^168+12x^169+24x^170+192x^171+78x^172+108x^173+420x^174+168x^175+246x^176+716x^177+378x^178+312x^179+1060x^180+360x^181+510x^182+1078x^183+570x^184+642x^185+1570x^186+690x^187+708x^188+1820x^189+648x^190+630x^191+1544x^192+606x^193+480x^194+1080x^195+498x^196+378x^197+634x^198+210x^199+198x^200+336x^201+114x^202+90x^203+180x^204+42x^205+36x^206+58x^207+12x^209+52x^210+50x^213+34x^216+24x^219+14x^222+6x^225+2x^228+4x^231+2x^234
The gray image is a linear code over GF(3) with n=282, k=9 and d=168.
This code was found by Heurico 1.16 in 11.1 seconds.