The generator matrix 1 0 0 0 0 1 1 1 1 1 0 2X 1 X 1 1 1 0 1 1 1 0 1 X 1 1 1 1 1 1 1 2X 2X 1 1 0 0 1 1 1 1 1 1 1 1 1 1 0 2X X 2X 1 1 X X 2X 2X 1 1 1 1 1 1 1 0 1 2X 0 1 2X 1 1 1 0 1 0 0 0 0 2X 1 2X+1 1 1 1 2X+1 1 X+1 X 2X+2 1 X+1 2X+2 X 1 2X 1 X X+2 2X+2 X+2 X+2 2 X+1 X 0 X+2 X+2 2X 1 1 2X+1 1 2 X+2 1 X+1 2X+2 2 2X+2 1 1 2X 1 0 2X+2 1 X 1 1 2 2 X 0 0 2X+2 X+1 1 2X 1 1 2 2X 0 0 0 0 0 1 0 0 0 2X+1 1 1 2X 2 X+2 X 1 X+2 X+1 2X+2 1 1 X X+1 X+2 0 0 2X+2 X 0 X+1 1 2X+2 2X+1 1 1 0 0 1 1 X 2X X+2 1 2X+1 X 1 2 X 2X+2 0 2X 1 2X+2 0 2X+2 2X 1 0 2X+2 2X+2 X X+2 X+1 1 X+2 0 1 X+1 2 2X+1 2X+1 0 2 0 0 0 0 0 1 0 1 2X+2 X 2X+1 2 2X+2 X+1 2X 2X+2 2X+1 X+1 X X 1 1 2X 2 2X+1 2X X+2 2X 2X+2 X+1 X X+1 X+2 X X+1 2X+2 2X+1 2X X+1 2 X 2X X+2 2 2X+2 X 1 2X 0 2X X+1 2X X 2 2X+2 1 1 2 0 X+2 1 2X 0 X+2 X+2 1 1 X+1 X+1 2X+1 1 1 X+1 0 0 0 0 0 0 1 2 2X+2 2X+2 X X 2 X+2 2X+1 2 2X 1 1 2X+1 X+1 X 2X 2X+1 1 2X+2 1 0 2 X 0 2 X+1 X+1 0 2X+1 X+1 2X+2 X+1 2 X+1 2 2X+1 2X+2 1 1 X+1 2X+1 0 2X+1 1 1 X+2 X+2 X+1 2X+2 X+1 X 2X+1 0 X+2 2 X+1 1 X+2 X+2 X+2 X+1 1 X+2 2X+1 0 X+1 0 0 0 0 0 0 0 2X X 0 2X X X 2X X 0 0 X 2X X 0 X 2X 0 0 2X 0 2X 2X 0 X 0 2X 0 0 0 X X X 2X 2X 2X 2X 0 X 0 2X 0 X 0 X 2X X 0 X 0 2X X 2X 2X X 0 2X X 2X 2X 2X 2X 2X X 2X 2X 0 0 0 generates a code of length 73 over Z3[X]/(X^2) who´s minimum homogenous weight is 123. Homogenous weight enumerator: w(x)=1x^0+30x^123+60x^124+102x^125+232x^126+354x^127+444x^128+756x^129+1296x^130+1320x^131+1964x^132+2562x^133+2340x^134+3410x^135+4002x^136+3852x^137+4826x^138+6270x^139+5874x^140+7438x^141+8556x^142+7380x^143+8568x^144+10416x^145+8436x^146+9372x^147+11052x^148+8208x^149+8540x^150+8718x^151+6858x^152+6622x^153+6366x^154+4224x^155+4278x^156+3864x^157+2202x^158+1954x^159+1476x^160+924x^161+778x^162+516x^163+270x^164+198x^165+90x^166+54x^167+50x^168+12x^169+16x^171+8x^174+4x^177+2x^180+2x^183 The gray image is a linear code over GF(3) with n=219, k=11 and d=123. This code was found by Heurico 1.16 in 547 seconds.