The generator matrix 1 0 0 0 1 1 1 2X 1 1 1 1 1 2X 1 1 0 1 1 0 X 1 1 1 1 1 1 0 1 1 X 1 2X X 1 1 1 1 1 2X 1 1 1 1 1 2X X 1 1 1 1 1 1 0 1 1 1 0 X 1 1 2X 0 1 1 X 1 1 1 1 0 1 0 0 0 1 2X+1 1 0 X 2X+2 2X+2 X+2 X 2X+1 2 1 X X 2X 1 X+2 2X+1 X 2X+2 1 2X+1 1 X 2 1 2X+2 1 1 2 2 X 0 0 1 X+1 X 0 X+1 0 1 1 2X+1 2X+2 2 2X X+1 2X+1 1 2X+2 2X+2 2X+2 2X 1 X 2X+2 1 1 2 1 0 2X+2 X+1 2X+2 0 0 0 1 0 1 1 2X+2 2X+1 X+1 2X+2 2X X+1 0 1 X+1 1 0 2X X+2 1 2X+2 X+2 X 2 2X 2X 0 2X+2 2X+1 X+1 1 2X+2 2 0 2 X+1 2X+1 1 2X+2 2 X+2 0 2X X+2 2X+1 2X 2 X+2 X X+1 X X+2 X+2 1 X 1 X+2 1 2X 2 0 2X+2 X+1 2X+2 X+1 1 0 X X+1 0 0 0 0 1 2 0 2X+2 2X+2 2X+1 2X X+1 2X 2 X+1 1 2 1 1 2X+2 2X+2 2X+2 X+1 X+2 X+1 X 2X+1 0 0 2X 1 X+1 X 1 2X+2 2X+2 2X+2 X+2 X 2 0 0 2 0 X X 1 2X+1 2 0 X+1 1 0 2X+1 2X X X+1 X 2X+1 2 2X 1 2X 2X+2 1 X+2 2X 2X+2 X+2 1 0 0 0 0 0 2X 0 2X 2X X 0 X 0 2X X X 2X X X 2X 2X X 2X X 0 2X 2X X 2X X 2X 0 2X 0 0 0 0 0 X X X X X 2X 0 X 2X 0 X X 0 2X X 0 X 0 0 X X 2X X X X X X X X 0 X 0 X 0 0 0 0 0 X X 0 2X 2X 2X 0 X X X 2X 0 0 2X 2X X 0 X 0 0 X 2X 0 0 X 2X 2X X X 0 X 2X X X 0 2X 0 X 0 2X X 0 0 0 0 2X X 2X 2X X 2X X 2X X 2X 0 X 0 0 X X X 2X X 0 generates a code of length 70 over Z3[X]/(X^2) who´s minimum homogenous weight is 123. Homogenous weight enumerator: w(x)=1x^0+106x^123+162x^124+222x^125+932x^126+492x^127+660x^128+1910x^129+942x^130+1110x^131+3154x^132+1404x^133+1518x^134+4162x^135+1824x^136+1836x^137+4758x^138+1830x^139+2064x^140+5400x^141+2178x^142+2214x^143+5354x^144+1902x^145+1644x^146+3618x^147+1368x^148+1134x^149+2234x^150+672x^151+576x^152+804x^153+264x^154+126x^155+254x^156+72x^157+12x^158+76x^159+12x^160+6x^161+18x^162+4x^165+8x^168+6x^171+4x^174+2x^177 The gray image is a linear code over GF(3) with n=210, k=10 and d=123. This code was found by Heurico 1.16 in 54.5 seconds.