The generator matrix 1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 X 1 1 1 X 1 1 1 0 1 1 1 1 1 0 1 1 X 1 1 1 1 1 0 1 1 1 2X X 1 X 1 1 X X 1 1 1 1 X 1 1 1 1 1 1 1 X 1 1 1 1 1 1 1 1 1 X 1 1 1 1 0 1 1 2 0 1 2 1 0 2X+1 2 1 0 X+1 X+2 1 1 X 2 2X+1 1 2 2X+1 0 1 2X+1 2 0 X+1 2X+2 1 0 2X+1 1 2 2X 2 X X+2 1 1 2X+2 X+1 1 1 2X+1 1 X+2 0 1 1 2 2X 1 2X 1 1 X+2 0 2X+2 1 X 2X 1 2X+1 2X 2X 1 X+1 X+2 X+1 X+1 X 1 2X+2 2X+2 0 0 0 0 2X 0 0 0 0 0 0 0 0 0 0 X 0 X 2X 0 X 2X X X X 0 2X 0 2X X 0 X 0 X 2X 2X 2X X X X X X 2X X 0 X X X X X X 0 X X 0 2X X 0 2X 0 0 2X X X 0 2X X 2X X 0 0 2X 2X 2X X 0 2X 0 2X 2X 0 0 0 X 0 0 0 0 0 0 0 2X 0 0 2X X 2X 0 2X X 0 X X 2X X 2X X 0 X 2X X 0 2X X X X X 0 0 2X 2X 2X X 2X X 0 0 X X 2X 2X 0 2X 0 X X 2X 0 X 0 0 0 X 2X 2X 2X X X 0 X 0 0 0 X 2X 0 X 0 0 0 0 0 X 0 0 0 X 2X 2X 0 X 2X 2X 0 0 2X X X 0 2X 0 X X 2X 0 X X 2X 2X 0 0 X 2X 0 0 0 0 X X 2X 2X X 2X 2X X 2X X 2X 0 0 X 0 X 0 2X X 2X X 2X 2X 0 2X 2X 2X 0 2X X 2X 2X X 0 2X X 0 2X X 0 0 0 0 0 2X 0 X 2X 2X 2X 2X 0 X 2X 2X 2X X X 0 0 X X 0 2X X 0 2X X 2X 2X X X 0 0 X 0 X 2X X 0 X X X 0 2X X 0 0 2X 0 X X 0 2X 2X 2X 0 0 0 2X X X 0 0 0 X 2X 2X 0 0 X 0 X 0 X X 0 0 0 0 0 0 0 X 2X 2X 2X 0 2X 2X 2X X 2X 0 2X 2X 0 2X 0 0 0 2X 0 0 X 0 X X X 0 X 2X X X 0 X X 0 0 2X 0 2X 0 X 2X 2X 0 X 2X 2X 2X 0 2X X 0 X 2X 2X 2X 0 2X 2X X 2X X 0 X 0 X X 2X 2X X 0 0 generates a code of length 78 over Z3[X]/(X^2) who´s minimum homogenous weight is 138. Homogenous weight enumerator: w(x)=1x^0+92x^138+6x^139+24x^140+310x^141+96x^142+150x^143+586x^144+222x^145+294x^146+798x^147+384x^148+444x^149+1214x^150+504x^151+522x^152+1516x^153+768x^154+810x^155+1854x^156+798x^157+786x^158+1726x^159+774x^160+666x^161+1278x^162+462x^163+450x^164+780x^165+270x^166+150x^167+344x^168+84x^169+66x^170+156x^171+6x^172+12x^173+120x^174+58x^177+44x^180+24x^183+20x^186+8x^189+4x^192+2x^198 The gray image is a linear code over GF(3) with n=234, k=9 and d=138. This code was found by Heurico 1.16 in 8.83 seconds.