The generator matrix 1 0 0 1 1 1 1 1 0 2X 1 1 1 1 1 1 0 1 1 1 1 0 2X 1 1 0 1 1 1 1 0 1 1 1 2X 1 2X 1 1 1 1 X 1 1 1 1 1 1 1 1 1 X 1 0 1 2X 0 0 1 1 0 1 2X 1 1 1 X 1 1 1 X 0 1 1 0 0 1 0 1 0 1 0 2 1 2 1 1 0 2X+1 2X+2 2X 1 2X+1 2X 2 0 X+2 1 1 1 2 X 1 2X+1 1 2X+2 2X 1 X+2 0 2X+1 1 2 1 2X+2 0 2X+2 X+1 1 1 2X+1 1 X 2X X+1 2X 2X 1 1 2X+2 0 0 1 0 0 X+1 2X+2 1 X+2 1 2X+1 X 2X+2 1 2X+1 2 X 1 1 X+2 X 1 1 0 0 0 1 2 1 2 1 0 2 2X+1 2 2X 2X+1 2X+1 1 2X+2 1 X+1 2X+2 2X+2 0 1 X X 2X X+2 X+2 1 2X+1 2 0 2X 2X+1 2X X+2 X+2 1 X 2X+1 X+1 0 2X+1 X+1 2 1 2X X+2 2X+2 2X+2 X 2X+2 X 2X 1 2X+2 2X+2 1 1 2X+2 2X+2 2X+2 X+2 2X+1 2X+1 2X+1 0 0 0 2X+1 2X X 2 X X 2X X+2 0 0 0 0 2X 0 0 0 0 0 0 0 0 2X 0 0 X 0 2X 0 X 2X 2X 2X 0 2X 2X X 2X 2X X X 2X X X 2X 0 X X X 0 X 0 X X X X X 0 0 X 0 X X 2X 0 2X X 0 2X X 2X 2X 0 0 2X 0 X 0 X 0 X 0 2X 2X 2X 2X 0 0 0 0 0 2X 0 0 0 0 0 X 2X 0 2X 0 0 0 0 X 0 X 2X 2X 0 0 X 2X X 2X 2X 0 2X X 0 X X X X X 2X 0 2X X 2X 0 2X 2X 0 2X X 2X 0 2X X X 2X X X X X 0 X 2X X X 2X 0 X 2X X 0 X X 0 X X 0 0 0 0 0 0 X 0 X X 2X X 2X 2X 2X X 2X X 0 2X 2X 0 2X 0 2X 2X 2X 0 X 0 2X X 0 X 0 0 2X 0 0 2X 2X X X X 0 X X 2X 2X X 2X 0 0 2X 0 X 2X X 2X X X 0 0 2X 0 0 2X 2X 2X 0 2X 0 0 0 2X 2X 0 2X 0 0 0 0 0 0 X X X X 0 0 2X X 0 0 2X X 2X 2X 2X X 0 0 X 0 2X 0 2X X 2X 0 X 0 0 X X 2X 2X 0 0 X 2X X 2X 2X 0 X 0 0 2X X 2X 0 2X 2X 0 X 2X 0 X X X 2X 2X X 0 2X 2X 0 0 X X 0 X 2X X generates a code of length 77 over Z3[X]/(X^2) who´s minimum homogenous weight is 135. Homogenous weight enumerator: w(x)=1x^0+144x^135+24x^136+126x^137+576x^138+318x^139+390x^140+1338x^141+618x^142+756x^143+2422x^144+924x^145+1056x^146+3158x^147+1476x^148+1548x^149+4270x^150+1890x^151+1962x^152+5004x^153+2202x^154+2358x^155+5340x^156+2274x^157+2148x^158+4350x^159+1656x^160+1584x^161+3120x^162+972x^163+702x^164+1800x^165+570x^166+336x^167+836x^168+156x^169+126x^170+256x^171+36x^172+24x^173+70x^174+6x^175+6x^176+42x^177+32x^180+18x^183+16x^186+10x^189+2x^195 The gray image is a linear code over GF(3) with n=231, k=10 and d=135. This code was found by Heurico 1.16 in 60.8 seconds.