The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 0 1 1 1 0 1 X 1 1 X 0 1 X X 0 X 0 0 2X 2X^2+X 2X^2+2X X 2X 2X^2+X 2X^2 0 2X^2+X 2X^2+2X 2X^2 X^2+X 2X 2X 2X^2+X X^2 2X^2+2X 2X^2+2X 2X^2+X X^2 0 X^2+X X^2+2X X^2+X 2X 2X 2X^2+X 2X^2+2X 2X^2+X 2X^2+2X X^2+X X^2 X X^2+2X 2X^2+2X X^2 X^2+2X 2X 2X^2 2X^2 2X^2 X^2 X^2+2X 2X 2X^2+X X^2+X 2X^2+X 0 0 X^2+2X X^2+X X 2X^2+2X 2X^2+X 0 2X^2+2X X 0 X^2 X 2X 2X X^2 X X^2+X 2X^2+2X 2X 2X^2+2X X^2+X X X 2X^2 2X^2 0 0 X 2X 0 X^2+2X X^2+X X X^2+2X 2X^2+2X X 2X^2 X^2+X X^2+X X^2+2X X^2 X^2 2X^2+2X 2X^2+2X 2X^2+X 0 2X^2+X 2X^2+X 2X^2+2X 0 2X^2 2X X^2+X X^2+X 2X X 0 X^2 2X^2+X 2X^2+2X X 2X^2 X 2X^2+2X 2X 0 X^2 2X 2X^2+X 2X^2+2X 0 2X X^2+X X^2+X X^2+2X X^2+2X X^2+X 2X X^2 2X^2+X 2X 2X 2X^2+2X 2X^2 X^2+X 0 X^2+X 2X^2+2X 2X X X^2 2X X^2 2X 2X^2+X X 2X^2 X^2+X X^2 0 2X 2X^2+X 0 0 0 X^2 0 0 2X^2 0 0 X^2 2X^2 X^2 2X^2 X^2 0 X^2 0 2X^2 0 2X^2 X^2 0 0 0 0 2X^2 0 2X^2 2X^2 2X^2 2X^2 2X^2 0 X^2 0 2X^2 2X^2 X^2 X^2 X^2 2X^2 2X^2 2X^2 0 2X^2 0 X^2 0 X^2 2X^2 2X^2 X^2 X^2 0 X^2 X^2 0 X^2 2X^2 2X^2 2X^2 0 0 X^2 0 2X^2 2X^2 2X^2 0 2X^2 0 X^2 X^2 X^2 0 2X^2 2X^2 0 0 0 0 X^2 2X^2 0 X^2 2X^2 0 2X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 0 2X^2 X^2 0 X^2 X^2 2X^2 2X^2 2X^2 X^2 2X^2 X^2 X^2 X^2 2X^2 2X^2 0 2X^2 2X^2 0 2X^2 2X^2 X^2 2X^2 2X^2 2X^2 2X^2 0 X^2 2X^2 X^2 2X^2 X^2 2X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 2X^2 0 0 2X^2 2X^2 0 0 0 2X^2 X^2 X^2 generates a code of length 77 over Z3[X]/(X^3) who´s minimum homogenous weight is 144. Homogenous weight enumerator: w(x)=1x^0+514x^144+18x^146+1220x^147+108x^148+306x^149+1432x^150+648x^151+2376x^152+2322x^153+1296x^154+3978x^155+1878x^156+864x^157+612x^158+808x^159+592x^162+390x^165+184x^168+106x^171+22x^174+6x^177+2x^207 The gray image is a linear code over GF(3) with n=693, k=9 and d=432. This code was found by Heurico 1.16 in 3.29 seconds.