The generator matrix 1 0 0 1 1 1 1 1 1 1 1 0 2X 1 2X 1 1 1 X 1 1 1 1 1 X 1 2X 1 1 0 2X 1 1 1 1 2X 1 X 1 1 1 1 1 2X 1 1 X 2X 1 1 1 0 1 1 0 1 1 1 1 1 1 0 X X 1 1 1 1 1 0 1 0 0 0 1 2 1 2X+1 2 2X+2 1 1 0 1 2X+2 2X+1 X 1 1 2X+1 2X 2X+2 X+2 2X X+1 1 2 2 1 0 X X+1 1 1 1 2X 1 0 2X+2 X X+2 X+1 1 0 0 1 1 2X+1 2X+2 1 1 2X+1 2X+2 1 2X+2 2X+1 X+1 2 X X X 2X 1 X+2 2X+1 2X X 0 0 0 1 1 2 2 2 1 2X 0 2X+1 2 2X+1 0 X+1 X+1 2X+2 X+2 X+2 2X+1 0 X+1 2X 2 1 2 2X X X+1 X+1 1 2X+1 0 1 2X+2 2X 0 2X+2 2X+2 2 1 2X+2 2X 1 0 2 X 1 X+2 2X+1 2X+1 2X 2 2X 2 2X+1 2 0 2 1 X 1 1 2X+1 1 0 2X+2 0 0 0 0 0 2X 0 0 0 0 0 2X 2X X 2X 2X X 0 2X 2X 2X X 2X 0 X 2X 0 X 0 X X 0 X 0 2X X 0 2X 0 0 X 2X 0 2X 2X 2X 2X 2X X 0 X X X 0 X 0 2X 2X 0 0 0 X X 2X 2X 0 0 X 0 X X 0 0 0 0 X 0 X 2X 2X 2X 2X 0 X X 2X X 0 2X 2X 0 X X X 0 X 2X X X 2X 0 0 0 0 2X X X 0 X X 2X 0 2X 0 0 2X X 0 X X 0 2X X 0 0 2X X 0 2X 0 X 0 0 2X X X 0 2X 0 2X 0 0 0 0 0 2X X X 0 X 0 X X X 2X 2X 0 X 0 X 2X X 0 X 0 0 X 2X X 2X 0 2X 0 X X 2X 2X 0 0 2X X X 2X X 2X 2X 0 0 2X 2X 2X 2X 2X X X 0 0 2X 2X X X 2X 0 2X 0 0 X 2X X generates a code of length 69 over Z3[X]/(X^2) who´s minimum homogenous weight is 123. Homogenous weight enumerator: w(x)=1x^0+52x^123+126x^124+222x^125+138x^126+558x^127+672x^128+254x^129+954x^130+1032x^131+266x^132+1224x^133+1206x^134+256x^135+1296x^136+1410x^137+340x^138+1344x^139+1512x^140+268x^141+1296x^142+1200x^143+212x^144+1008x^145+936x^146+184x^147+606x^148+426x^149+98x^150+270x^151+126x^152+44x^153+54x^154+6x^155+26x^156+12x^157+16x^159+18x^162+6x^165+2x^168+6x^171 The gray image is a linear code over GF(3) with n=207, k=9 and d=123. This code was found by Heurico 1.16 in 6.54 seconds.