The generator matrix 1 0 0 1 1 1 1 X 1 1 2X 1 1 1 0 1 1 1 1 1 1 1 X 2X 1 0 1 0 1 1 1 1 1 1 1 2X X X 2X 0 1 1 1 1 1 1 1 2X 1 1 1 1 1 1 0 1 2X 1 0 1 0 0 1 1 1 1 1 1 1 0 1 0 0 0 2X+1 1 1 2X+2 2X+1 1 2 2 X 2X 2X X X+2 2 1 X+1 1 1 1 2 1 0 1 X 2X+2 X+1 2X 2X+2 X+2 2X+2 1 1 1 2X 2X X+1 X+2 0 X 1 2X+1 X 1 2 0 2 2X+2 1 0 0 X 1 X+1 1 2 X 1 X 2X+1 2 2X+1 X X+2 2 0 0 1 1 2 2X+2 1 X+2 2X+1 2X 1 X X+2 X+2 1 0 X+1 1 2 X+1 X X+2 2X+2 0 2X 2X+1 2X+1 0 2 2X+1 2X+1 2X 2X+2 0 2 2X+1 X X+2 1 1 1 2X+1 0 1 X+2 2X 2X+2 2X+1 X 2X+1 2X+2 2X+1 1 2 1 0 2X+1 0 X+1 2X 1 X+1 X+2 X+1 2X+2 2X 2X X+2 X 0 0 0 2X 0 0 0 0 0 2X X 0 0 0 X 2X X X X 0 X X 2X X X 2X 2X 0 0 0 2X 0 X 2X 2X 0 2X X 2X X X X X 0 X 0 X 0 2X X 0 2X X 2X 2X X X 0 X 0 0 2X 2X 0 X X 0 2X 2X 0 0 0 0 X X X 0 X 0 X 0 2X 0 X 0 X X X 2X 0 0 X 0 0 2X 2X 2X 2X 2X 0 2X 0 2X X 2X 2X 0 X 0 X 0 X X 2X 2X X X X 2X 0 2X 0 0 0 2X 0 X X X X X X 2X 2X 2X 0 0 2X generates a code of length 69 over Z3[X]/(X^2) who´s minimum homogenous weight is 128. Homogenous weight enumerator: w(x)=1x^0+336x^128+296x^129+684x^131+354x^132+732x^134+354x^135+648x^137+376x^138+732x^140+266x^141+480x^143+222x^144+366x^146+134x^147+240x^149+94x^150+120x^152+60x^153+36x^155+20x^156+4x^159+2x^162+2x^168+2x^174 The gray image is a linear code over GF(3) with n=207, k=8 and d=128. This code was found by Heurico 1.16 in 17.2 seconds.