The generator matrix 1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 X 1 1 1 1 0 1 1 1 1 0 1 1 X 2X 1 1 1 1 2X 1 1 1 1 1 1 1 1 1 1 2X 1 1 X X 1 1 1 2X 1 1 1 1 1 2X 1 2X 0 1 1 0 1 1 2 0 1 2 1 0 2X+1 2 1 0 X+1 2 1 1 2X+1 2 0 X+2 1 0 2X+1 2 X+1 1 X+2 X 1 1 2X+1 0 X+2 2X 1 2X+1 2X+2 1 2X+2 X+2 2X X 2X 2X+1 X 1 2 X+1 1 1 X+1 2X 0 1 2X 2 2X 1 X+2 1 X+1 1 1 X+2 0 0 0 2X 0 0 0 0 0 0 0 0 0 0 X X 2X 2X X 2X 2X X 2X X X 0 2X 0 2X 2X 2X 0 2X 2X 0 0 2X 0 2X X 2X 0 X X X X 0 2X 2X X 2X 2X 2X 0 0 0 0 X X X 2X 2X X 0 X 0 0 0 0 0 X 0 0 0 0 0 0 0 2X 0 0 2X 2X X 0 2X 2X 2X X 2X 0 2X 0 X 2X X 0 X 2X 0 X X 0 X 2X 2X 2X X 2X 2X X 0 0 0 0 2X 0 2X X 2X 2X X 0 2X X 2X 0 2X 0 2X 2X 0 0 0 0 0 0 X 0 0 0 X 2X 2X 0 X 2X X 0 0 X 2X 2X 0 0 X X 2X X X 0 2X 2X 2X 0 X 0 2X X 2X X X X 2X 2X X 2X 0 2X 0 0 0 2X 0 0 X 2X 2X X 0 2X X X 2X 2X 0 2X 0 0 0 0 0 0 0 2X 0 X 2X 2X 2X 2X 0 X 2X X 0 2X X 2X X X X X 0 0 2X 2X X 2X 2X 0 0 X 0 0 X X 0 0 0 X X 2X 2X X 0 0 X X X X 2X 0 0 X 0 0 2X X 2X X X 2X 0 0 0 0 0 0 0 0 X 2X 2X 2X 0 2X 2X 2X 0 2X X X 0 0 0 X 2X 2X 2X 0 X X 0 0 2X 0 X 2X X X X X 0 0 0 0 X X 0 2X 2X X X 2X 0 0 0 X 2X 2X X 0 X X 2X X 0 0 0 X generates a code of length 66 over Z3[X]/(X^2) who´s minimum homogenous weight is 114. Homogenous weight enumerator: w(x)=1x^0+54x^114+12x^116+204x^117+72x^118+126x^119+526x^120+168x^121+216x^122+852x^123+330x^124+438x^125+1208x^126+600x^127+624x^128+1626x^129+738x^130+870x^131+1830x^132+1032x^133+780x^134+1924x^135+690x^136+732x^137+1362x^138+486x^139+420x^140+718x^141+204x^142+120x^143+304x^144+42x^145+30x^146+124x^147+12x^148+6x^149+84x^150+56x^153+26x^156+24x^159+2x^162+8x^165+2x^168 The gray image is a linear code over GF(3) with n=198, k=9 and d=114. This code was found by Heurico 1.16 in 7.15 seconds.