The generator matrix 1 0 0 0 1 1 1 1 0 1 1 1 1 1 0 1 1 2X 1 1 1 1 1 2X 1 1 2X X 1 1 2X 2X 1 0 1 1 1 1 1 1 1 1 1 1 1 X 0 1 1 1 1 1 0 1 1 1 0 1 1 1 X 0 1 1 1 1 1 1 1 1 1 0 2X 0 1 X 1 1 1 1 1 1 2X 1 1 1 2X X 2X 2X 1 0 1 0 0 0 0 2X 2X 2X 2X 2X 2X 0 1 1 2 X+1 1 X+1 2X+2 1 1 X+1 X X+2 2X+2 1 1 2X+2 X+1 1 1 X+1 1 X 2 2X+1 2X X+2 0 X+1 2 2X 2X+2 X+2 1 1 1 X+1 X 2 2 1 2X 2X+1 2 X 2X+1 2X+2 2X+2 1 1 X+2 2 1 X+2 2X+1 2X+2 0 X 1 1 1 1 X+2 2X 0 2X+1 X+2 X+1 2X+1 X+1 1 2 2X+2 2X 1 1 1 1 X 0 0 1 0 0 1 2X+2 2X+1 1 2 0 2X+1 2 2X+1 X+1 X X+2 2X+1 X 1 X+2 2X+2 2X+1 1 X+2 1 2X+2 X+1 0 2X 2X+2 X 0 X+2 0 2 2X+1 1 0 1 X+1 2X+2 X 0 2X 2X X+1 X X+1 2X+1 X+1 2X+1 2 2X 2 0 1 2X+1 X 2X+1 X+1 X+1 X+2 X+1 X 2X+2 2X+2 1 2X+1 X 2 2 2X 2X 2 1 1 X+2 2 X 0 X+1 2X+1 2 2X+1 2 2X 2 0 X+2 X 0 0 0 1 1 X+1 2X+1 2 2 0 X+2 0 2 2X 2 X+2 2X+2 X 2X 2X+2 X+1 0 X+2 2X+1 2X+1 1 X+2 2X+1 X+1 X+1 X+1 X+1 X+2 X 2X+1 2 2X+1 2X+2 X X+1 2 0 X 2X+2 X X 2X+1 X+2 X X X+1 2X+2 2 2X+2 2X+1 1 0 2 2 2X+2 X+2 0 2X+1 0 X 1 0 X X 2X 1 2X 1 2 X 2X+1 2X+1 2 2X X X+1 0 2 2 0 1 X+2 X+2 2 X+2 X 0 0 0 0 2X 2X 2X X X 2X X 0 X 0 X X X 0 0 X 2X 0 X 2X 0 0 2X 0 X 0 X 0 2X 2X X 0 X 2X X 0 2X X X 0 2X 2X 2X 0 X 2X 2X 0 0 0 0 0 2X 0 2X 2X 2X X 2X X X X 2X 2X X 2X X 2X X X 0 2X X 2X 2X 2X 0 2X X X 0 0 X X 0 X 2X generates a code of length 91 over Z3[X]/(X^2) who´s minimum homogenous weight is 168. Homogenous weight enumerator: w(x)=1x^0+322x^168+234x^169+414x^170+584x^171+582x^172+654x^173+962x^174+840x^175+738x^176+1114x^177+738x^178+864x^179+992x^180+750x^181+744x^182+1022x^183+840x^184+810x^185+956x^186+678x^187+564x^188+796x^189+468x^190+504x^191+620x^192+312x^193+306x^194+386x^195+234x^196+138x^197+142x^198+102x^199+78x^200+94x^201+24x^202+18x^203+12x^204+24x^205+14x^207+6x^208+2x^210 The gray image is a linear code over GF(3) with n=273, k=9 and d=168. This code was found by Heurico 1.16 in 9.11 seconds.