The generator matrix 1 0 0 1 1 1 1 1 0 2X 1 1 1 1 1 0 1 1 1 1 1 2X 1 X 1 X 1 1 1 1 X 2X 1 X 1 2X 1 1 1 1 1 1 X 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 2X X 0 1 1 1 1 1 X 1 0 X 0 2X 1 0 1 0 1 0 2 1 2 1 1 0 2X+1 2X+2 2X 1 2X 0 2X+1 X+2 2X+2 2X+1 1 0 1 2 1 2X+1 2 2X+1 2 1 1 2X 1 X+1 1 0 1 2X+2 2X+2 X 0 1 1 2X 0 X+1 2X 2X+2 1 X 2 X+1 2 2X+1 X+1 2X+1 X 1 0 1 1 X 0 X+2 X+1 0 X+2 1 1 1 1 2 0 0 1 2 1 2 1 0 2 2X+1 2 2X 2X+1 2X+1 1 1 X+2 2X+2 X 2X+1 X X+1 X X+2 2X+2 0 0 X 2X+2 2 2X+1 0 X+2 2X+2 X+1 2 X 2 0 X+1 1 X 2X+1 2X+2 2X 0 2X 2X 2 0 2X+2 2 X+1 0 1 0 0 2X+1 X 1 2X 2X 1 1 2X X+2 1 0 0 2X+2 2 X X 0 0 0 2X 0 0 0 0 0 0 0 0 2X 0 0 0 0 X 0 X 2X X 2X 2X X X 2X X X X X 2X X 2X X X 0 X X 2X 2X 2X 0 0 2X 0 0 X 2X 0 0 X X 0 X 0 X X 0 X X 2X 2X 2X 2X X 2X X X 0 0 X X 0 0 0 0 2X 0 0 0 0 0 X 2X 0 2X 0 0 X 0 X 0 X 2X X 2X X X X 2X X 2X X 0 2X 0 X 0 2X 2X X X 2X 0 2X 2X 0 0 X 2X 0 2X 0 X 0 X 0 2X 0 0 2X X X 2X X 2X 0 X X X 2X X X X 2X 0 0 0 0 0 X 0 X X 2X X 2X 2X 2X X X 2X 2X X X X 2X 0 0 2X 2X 0 2X X 0 X X 2X 0 2X 0 X 0 X X 2X 2X 0 0 0 X 0 0 X X X 2X 2X 0 0 0 2X X 0 X 0 0 X 2X X X 0 0 2X 2X 2X X 0 0 0 0 0 0 0 X X X X 0 0 2X X 0 2X 2X 0 2X 2X X X X 2X 2X 0 0 X 0 0 0 X 2X X X 0 0 X 0 X X X 2X X X 2X 0 0 X 2X X 0 X X 0 X 2X 0 X X X X 2X 2X 0 X 2X 0 0 X 0 X X generates a code of length 73 over Z3[X]/(X^2) who´s minimum homogenous weight is 127. Homogenous weight enumerator: w(x)=1x^0+30x^127+96x^128+256x^129+162x^130+540x^131+722x^132+420x^133+1230x^134+1148x^135+732x^136+1866x^137+1800x^138+1344x^139+2958x^140+2324x^141+1902x^142+3762x^143+2854x^144+2376x^145+4416x^146+3212x^147+2046x^148+4374x^149+2840x^150+1902x^151+3588x^152+2258x^153+1212x^154+2124x^155+1200x^156+714x^157+972x^158+634x^159+204x^160+270x^161+216x^162+78x^163+30x^164+96x^165+12x^167+58x^168+6x^170+26x^171+22x^174+10x^177+4x^180+2x^183 The gray image is a linear code over GF(3) with n=219, k=10 and d=127. This code was found by Heurico 1.16 in 73.6 seconds.