The generator matrix 1 0 0 1 1 1 1 1 0 2X 1 1 1 1 1 0 1 1 1 1 1 1 2X 1 X 0 1 0 1 1 1 1 X 1 0 1 1 2X 0 1 2X 1 1 2X 1 1 1 0 1 1 1 1 1 X 1 0 X 2X 1 1 1 1 1 1 1 1 0 1 2X 1 1 1 0 1 0 1 0 2 1 2 1 1 0 2X+1 2X+2 2X 1 2X 0 X+1 2X+2 1 2 0 1 2 1 1 2 1 X X+2 2X+1 X+1 X 2X+1 1 2 X 1 0 0 1 2X+1 0 1 2 2X X+1 1 X+2 1 2X 2 X 1 0 1 2X 2X X+1 X 2X X+1 X X+2 2 1 1 2X 1 2X+1 1 2X+1 0 0 1 2 1 2 1 0 2 2X+1 2 2X 2X+1 2X+1 1 1 X+2 2 X+1 0 X 0 2 2X+2 1 2X 2X+1 2 0 X X X+2 1 1 X+1 X+2 2X+2 0 1 2X 1 2 X+1 2X+1 2X 2 2X X 2X+2 2X+2 2X+1 2X+1 2X X 0 0 1 1 2X+1 X+2 X+1 2 X+1 2X 2X+1 X+2 X 2X 2X+2 X+1 2X X 0 0 0 2X 0 0 0 0 0 0 0 0 2X 0 0 0 0 2X 2X 2X 2X 2X 2X X X X 2X X X X 2X 2X X X 0 0 X X 2X X 0 2X X X 2X 2X X 2X 2X 0 X 0 0 0 2X X X 2X 0 2X X 0 X 2X X 0 X 0 0 0 0 2X 0 0 0 0 2X 0 0 0 0 0 X 2X 0 2X 0 0 X 0 0 X 2X 2X X X 2X 2X X 2X 2X 2X 2X 2X X 2X 2X X X 0 0 0 2X X 0 X X 0 0 2X 2X 0 0 2X X 2X 2X 0 X 2X X 2X 0 2X 2X 0 0 2X X 0 0 0 2X 0 0 0 0 0 0 X 0 X X 2X X 2X 2X 2X X X 2X X 0 2X 2X X 0 X 0 X 0 X X 2X X 2X 2X 2X 0 X X 2X 0 2X 2X X X X 0 0 2X 2X X 0 2X 0 0 X 2X 2X 0 2X 0 X X X X 0 2X 0 2X X 2X X 2X 2X 0 0 0 0 0 0 X X X X 0 0 2X X 0 2X 2X 2X X 0 2X X 2X 0 0 2X X 0 2X X 0 0 2X X X 2X X 2X X 2X 0 2X X X 2X X X X X 0 X 0 2X 2X X 0 2X X X 0 2X X X X 0 X X 2X 0 X 2X X generates a code of length 72 over Z3[X]/(X^2) who´s minimum homogenous weight is 126. Homogenous weight enumerator: w(x)=1x^0+134x^126+96x^127+336x^128+530x^129+288x^130+768x^131+970x^132+738x^133+1902x^134+1614x^135+1242x^136+2592x^137+2088x^138+1494x^139+3702x^140+2682x^141+2118x^142+4278x^143+3262x^144+2358x^145+4236x^146+3074x^147+2052x^148+3936x^149+2468x^150+1380x^151+2604x^152+1548x^153+930x^154+1362x^155+728x^156+324x^157+450x^158+318x^159+84x^160+72x^161+126x^162+18x^163+6x^164+46x^165+34x^168+36x^171+14x^174+8x^177+2x^180 The gray image is a linear code over GF(3) with n=216, k=10 and d=126. This code was found by Heurico 1.16 in 56 seconds.