The generator matrix 1 0 0 1 1 1 1 1 0 2X 1 1 1 X 1 1 1 1 1 0 0 1 1 1 1 0 1 1 1 2X 1 2X 2X 1 1 1 1 1 1 X 1 0 0 1 0 1 1 0 2X 0 1 2X 1 1 1 0 1 1 1 X 1 X 0 1 0 2X X 1 0 1 0 1 0 2 1 2 1 1 0 2X+1 2X+2 1 0 2X+1 2X+1 2X 0 2X 1 2X+2 2 X+2 2X+1 1 X 1 0 0 1 1 1 2X+2 X+1 X+2 2X 2X+1 X+2 2X X+1 1 1 0 1 X+2 X+1 1 1 1 2X+2 2X 2X 2X+1 2 1 0 X 0 1 2X+2 1 1 1 0 1 1 0 0 0 1 2 1 2 1 0 2 2X+1 2 2X 2X+1 1 0 2X+2 1 2X+1 2 1 X 2X+1 X X+2 2X 2 2X+1 0 0 1 X+2 2 X X+2 1 0 2 1 2X+1 1 X+2 2 2X 1 2X 0 1 2X+1 X+2 X+2 2X+1 1 1 2X+2 2 2 2X+1 X+2 1 1 X+2 2X+1 2X+2 2X+1 1 X+2 0 0 0 0 0 2X 0 0 0 0 0 0 0 0 2X 0 0 X X X X 2X 2X 2X X 2X 0 2X X X X 2X X 2X 0 X 0 2X X 0 X X 2X 0 2X 0 0 X 2X 2X 2X X 2X 2X 0 0 2X 2X 2X 0 2X 2X 0 2X X 0 X 0 0 X 0 0 0 0 2X 0 0 0 0 0 X 2X 0 0 X X 0 X 2X 0 0 X 0 2X X 2X 2X 0 2X X X 0 0 X 2X X 0 2X 2X X 2X 2X 2X X 2X 2X 0 X X X 2X 0 X X 2X 2X X 0 2X 2X 2X X 0 0 2X 0 X 2X 0 0 0 0 0 X 0 X X 2X X 2X 2X 0 2X X 0 0 X 2X 0 0 X 0 X 0 2X 2X 0 X 2X 0 X 0 2X 2X X 0 X 2X 0 X 2X X X X 2X 2X X X X 0 X 2X 2X X X X 2X 2X X 0 X X X 0 0 2X 0 0 0 0 0 0 X X X X 0 0 2X 2X X 0 2X 0 0 0 2X 0 2X 0 0 X X 2X 0 X 2X X 2X 2X X 0 X X 0 2X 2X X 2X 2X 0 X 0 X 2X 2X 2X X 0 0 0 2X 2X X X 0 2X 0 2X 0 X 0 0 X generates a code of length 68 over Z3[X]/(X^2) who´s minimum homogenous weight is 117. Homogenous weight enumerator: w(x)=1x^0+60x^117+36x^118+54x^119+548x^120+234x^121+318x^122+1122x^123+612x^124+504x^125+2088x^126+1002x^127+1188x^128+3478x^129+1422x^130+1584x^131+4074x^132+1950x^133+2256x^134+5518x^135+2160x^136+2478x^137+5580x^138+2286x^139+2232x^140+4756x^141+1734x^142+1572x^143+3168x^144+1044x^145+642x^146+1504x^147+486x^148+240x^149+536x^150+132x^151+42x^152+184x^153+24x^154+12x^155+110x^156+38x^159+20x^162+12x^165+4x^168+4x^171 The gray image is a linear code over GF(3) with n=204, k=10 and d=117. This code was found by Heurico 1.16 in 51.5 seconds.