The generator matrix 1 0 0 0 0 1 1 1 2X 0 2X 2X X X 1 1 0 X 1 1 1 1 1 1 1 1 1 X 1 1 1 X 1 1 1 1 1 1 1 1 1 0 1 1 0 X X 1 1 2X 0 1 1 2X 1 1 X 0 1 1 1 2X 1 1 1 1 1 1 2X 1 1 X 1 1 1 2X 1 1 0 1 0 0 0 0 0 0 0 1 1 1 1 1 2X X 2X 2X 2 2X+1 2 X 2 2X+2 0 X+2 2X+2 1 X+2 1 X+2 2X 2X+1 2X+1 2X+1 2X+1 2X X+1 2 X+2 2X+1 1 0 1 0 1 2X 2X+2 1 1 1 2X 1 2X X+2 2 1 1 X+1 2X+2 2X+2 1 X+2 2X X+1 2X+1 X 1 0 2 2X 1 2X 2X+1 X+2 1 X+1 X+1 0 0 1 0 0 0 1 2X+1 1 1 2X 2X+1 2X+2 2X+2 2 2 1 1 1 1 X 2X+1 2X+1 X X 2X X+1 2 X+2 0 X+2 X 2X 0 2X X 2 X+1 1 X 2X+1 1 X+2 X+2 1 2X 1 1 X+1 X+2 2X+2 2 2 1 2X+2 2 2 1 X+2 2X X 0 2 0 0 2 2X+2 X+2 0 0 0 X+2 2X+2 X+1 0 X+1 X+1 2 0 0 0 1 0 1 1 2X+2 X+1 X+1 2X+1 X+2 X 2X+2 0 2X+2 2X+1 X+2 2X+1 2 X X 0 X+1 X+2 X X+1 X X+1 2 2X+2 1 2X X X+2 X+1 X 1 2X+2 2 X+2 X+1 2X+2 X+1 2X 2X+2 1 0 X+2 X+1 1 2X+1 0 0 2X+1 X+2 2X 2X+2 X+2 1 2X 0 X 2X 2X+1 2X+2 2X+1 X+1 0 X+2 1 X X 2X 2 X+2 2X 2X 0 0 0 0 1 2 X 2X+2 2 X X+2 2 2X+2 0 2 X 1 0 2 X 2X+2 2X+2 0 1 X+2 1 2X+1 2X+1 2 X+1 2X+2 2 2X X+1 2X 1 0 2 2X+1 2X+1 2 X+1 2X+1 2X+2 2X+2 X+2 2X X+1 2X+1 X+1 2 X+1 1 0 0 X 2X 2 X 2X 2X+1 2 2X X+1 2X+1 2 1 2X+2 1 2 1 0 X+1 0 0 1 2X 2 0 0 0 0 0 2X 0 2X 0 0 2X 2X 2X 0 2X 0 0 2X 0 2X 0 X X 2X X 0 0 0 2X 2X X X 2X X 0 0 X X X 0 X 2X 2X 2X 2X 0 X 0 0 0 X 2X X 2X 2X X 0 0 2X 0 X X 2X X X 0 0 0 X 2X X 2X 0 X 2X 0 2X X generates a code of length 78 over Z3[X]/(X^2) who´s minimum homogenous weight is 137. Homogenous weight enumerator: w(x)=1x^0+306x^137+426x^138+516x^139+1560x^140+1526x^141+1230x^142+3198x^143+2860x^144+2382x^145+5544x^146+4362x^147+3438x^148+7542x^149+6602x^150+4590x^151+9882x^152+8516x^153+5748x^154+12192x^155+9322x^156+6510x^157+12828x^158+9086x^159+6030x^160+10686x^161+7374x^162+4362x^163+7716x^164+5064x^165+2808x^166+4524x^167+2646x^168+1200x^169+1914x^170+906x^171+414x^172+648x^173+260x^174+120x^175+168x^176+58x^177+18x^178+24x^179+20x^180+4x^183+4x^186+6x^189+2x^192+4x^195 The gray image is a linear code over GF(3) with n=234, k=11 and d=137. This code was found by Heurico 1.16 in 570 seconds.