The generator matrix 1 0 0 1 1 1 1 1 0 2X 1 1 1 X 1 1 1 1 1 1 0 1 2X 1 0 1 1 1 2X 1 X 1 1 1 1 1 2X 0 0 1 1 1 X 2X 1 1 0 1 1 X 1 1 1 1 1 X X 1 1 1 0 1 1 1 1 1 0 1 0 1 0 2 1 2 1 1 0 2X+1 2X+2 1 X 2X+1 1 2 0 X+2 2X 2X 1 2X+2 1 X+1 2X+2 X X 2 1 X X+2 2X+1 2X+1 2X+2 1 1 0 2X+1 1 2X 1 1 0 2X+2 X 2 2X+2 1 2X 2X+2 1 2 1 1 1 X+2 2X+1 1 X 2X+2 X 2X 1 0 0 0 1 2 1 2 1 0 2 2X+1 2 2X 2X+1 1 2X+2 2X+2 1 2X X 2 1 2X+1 2X+2 2X+1 X X 2X+2 2X 1 1 0 2X+2 0 0 2X+1 X+1 2X+2 0 1 2X 2X+2 1 2 1 X+1 2X 1 X+2 2X+2 2X+1 2X+2 0 0 X X+1 2X+2 1 0 0 X+1 1 2 X 2X+2 2 0 0 0 0 2X 0 0 0 0 0 0 0 0 2X 0 0 X X X X X X 2X X X X 2X 0 X 0 2X 0 X X X 2X 0 X 2X 2X X X 0 2X 2X 2X 2X X 0 0 X 2X X X 0 X X 2X 0 0 0 2X X 2X X 2X 0 0 0 0 0 2X 0 0 0 0 0 X 2X 0 0 2X X 0 0 0 0 0 2X 0 2X X X X 2X 2X 2X 2X 2X 2X X 2X 2X X X X 0 2X X X 2X X 0 0 2X X X X X X 2X 2X X X 2X X 0 0 2X 0 0 2X 2X 0 0 0 0 0 X 0 X X 2X X 2X 2X 0 X 2X X 2X X 2X X 2X 2X X 2X 2X 2X X 0 X 0 0 0 X 2X X 0 X 2X 2X 2X 2X X 2X X X 0 2X 0 0 X 0 0 X 0 X 2X 2X 2X 0 2X 0 0 X X 0 0 0 0 0 0 0 X X X X 0 0 2X 2X 0 0 0 0 2X 2X 2X X 0 2X 2X X 0 0 2X X X X X 0 0 2X X X 0 X 2X 2X 2X 2X 2X X 0 0 X 2X 0 0 2X X 2X 0 0 2X 2X 2X 2X 2X 2X 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+132x^114+48x^115+240x^116+430x^117+336x^118+888x^119+810x^120+702x^121+1362x^122+1582x^123+1152x^124+2688x^125+2128x^126+1668x^127+3762x^128+2848x^129+2040x^130+4644x^131+3486x^132+2250x^133+4758x^134+3128x^135+2244x^136+3798x^137+2514x^138+1536x^139+2574x^140+1496x^141+762x^142+1098x^143+654x^144+288x^145+354x^146+274x^147+96x^148+60x^149+84x^150+18x^152+48x^153+30x^156+22x^159+10x^162+4x^165+2x^168 The gray image is a linear code over GF(3) with n=198, k=10 and d=114. This code was found by Heurico 1.16 in 50.1 seconds.