The generator matrix 1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 X 1 1 1 1 1 0 1 1 0 1 1 1 1 0 1 0 1 1 1 X 1 1 1 1 1 X 1 1 1 1 X X 1 1 1 X 1 1 1 1 1 0 1 1 0 1 1 1 0 1 X 1 0 1 1 2 0 1 2 1 0 2X+1 2 1 0 2 2X+1 1 2X+1 1 2 0 X 2 2X+1 1 2X+1 0 1 2 2X 2X+1 2 1 X+2 1 1 0 2X+2 1 X+2 X+1 X X 2X+1 1 2X+1 X+2 X X 1 1 X+1 0 X+1 1 1 X 2X+2 2X X+1 1 X+1 1 1 2X+1 2X 0 1 0 0 0 0 0 2X 0 0 0 0 0 0 2X X 2X 2X 2X 2X 0 X 2X X 0 2X 2X 2X 2X 2X X 0 2X 0 2X 0 0 0 2X 0 0 X 0 2X X 2X 0 X X 0 0 2X 0 2X 2X X 0 0 X 2X 2X 0 0 0 X X 0 X 2X X 0 X X 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 2X X X 2X 2X X X 0 2X X 0 X X 0 0 0 2X 2X 2X 2X 0 2X X X 0 X 0 X X X 0 X 2X 2X X 2X 0 X 0 X 0 2X X 0 2X 0 2X 2X X 2X 2X 2X X X X 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X 2X 2X 2X 2X 2X X 2X X X X 2X 2X X X 2X X X 0 2X X X 2X X 0 2X X 0 X X 0 X 2X X 2X 0 0 0 X 0 X 2X 2X 2X 0 X 0 0 0 X 0 0 0 0 0 0 2X 0 0 X 2X 2X X 2X 0 2X 2X X 2X 2X X 0 2X 0 2X 0 2X 0 X 2X 0 2X 0 2X 0 0 X 0 0 X 0 X X X 0 2X X 0 X 0 2X 0 2X 0 2X X X 2X 0 2X 0 0 2X 2X 2X 0 0 X 2X X 2X 0 0 0 0 0 0 X 0 X 0 X X X 2X 2X X X 0 0 X 2X 2X 2X 0 X 0 X 0 2X 2X X 2X X 0 X 2X 0 0 X 2X X 0 X X 0 0 X X X 2X 0 0 0 X 2X X X X 2X 0 0 2X X 0 0 X 2X 0 X 0 0 0 0 0 0 0 0 X X X X 0 2X X 2X 0 2X 2X 0 0 2X X 2X 2X 0 2X X 0 2X X 2X X 0 X 0 0 X 2X X 0 0 0 2X X X X 0 2X 2X 0 0 X 2X X 0 2X 0 X 0 X 0 2X 2X X 0 0 2X 2X 0 0 generates a code of length 70 over Z3[X]/(X^2) who´s minimum homogenous weight is 117. Homogenous weight enumerator: w(x)=1x^0+82x^117+18x^119+236x^120+36x^121+132x^122+348x^123+180x^124+372x^125+472x^126+480x^127+876x^128+436x^129+1458x^130+1686x^131+528x^132+2298x^133+2832x^134+550x^135+4002x^136+4350x^137+538x^138+5202x^139+5076x^140+558x^141+5214x^142+4632x^143+610x^144+4038x^145+3414x^146+550x^147+2178x^148+1830x^149+478x^150+894x^151+750x^152+384x^153+228x^154+252x^155+306x^156+36x^157+24x^158+214x^159+134x^162+90x^165+34x^168+8x^171+4x^174 The gray image is a linear code over GF(3) with n=210, k=10 and d=117. This code was found by Heurico 1.16 in 62 seconds.