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 X X 1 1 1 X 1 1 1 X 1 1 1 1 1 1 1 1 X 1 1 X 1 1 1 0 X 0 0 0 0 0 0 0 0 0 0 0 0 X 2X 2X X 2X 2X 2X X 2X X X X 0 X X X X 0 X 2X X 2X 0 X 2X 0 0 2X 2X 2X 2X X X 0 0 X X X X X 2X 2X X X X X 0 0 X 0 2X X X X 2X 2X 2X X 2X X 0 0 X 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 X 2X 2X 2X 2X 0 X 0 X X 2X 2X 0 0 X X X 0 X 2X X 0 0 X 2X 2X 0 0 X X 2X X X X X 0 2X 0 0 X 0 0 X 2X X 0 2X 2X 0 0 X 0 2X X X X 0 2X X 2X X X 2X 0 X 0 X 2X X X 0 0 0 X 0 0 0 0 X 2X 2X 2X 0 0 X 0 X 2X X 2X 2X 2X 0 0 X 2X 0 0 0 X X 2X 0 X 0 2X 2X 0 X X 0 X X 0 X 0 0 2X X 0 X 2X X X 2X X 0 2X 0 X X X 2X 2X 0 X 0 2X 2X 2X 0 X 0 0 X 0 X 0 X X 0 0 0 0 0 X 0 0 X 2X 0 2X 0 0 2X 2X X X X 2X X 0 2X 2X 0 2X X 2X 2X X X 0 2X X X X 0 X 0 0 0 0 X 0 X 2X 0 X 2X X X 2X 2X 0 X 0 0 2X 0 0 X 2X 0 0 2X X 0 2X X X X 0 X 2X 0 0 2X 0 2X X 2X X 0 0 0 0 0 X 0 2X 2X X 0 2X 2X 2X 2X 2X 2X 0 X 0 0 2X 0 X 2X X 2X 2X 2X 2X X X X 2X 0 2X 0 2X 2X 0 0 X 0 0 X 0 0 0 X X 2X 0 0 0 X 2X X 0 X 2X X X 0 2X X 0 0 2X 2X 2X X 0 X X X 0 X 2X X X 2X 0 0 0 0 0 0 X 2X 2X 2X 2X 2X 2X X X X 0 2X 0 0 X 0 2X 2X 2X 0 X 2X 2X 0 0 X 0 X 2X 2X 0 2X 0 X 2X X X 2X 0 0 0 0 2X 2X X X 0 0 X 2X 2X X 0 2X X 2X 2X X 0 2X 0 X X 0 0 2X 0 2X X 2X 2X 0 2X 2X X generates a code of length 81 over Z3[X]/(X^2) who´s minimum homogenous weight is 144. Homogenous weight enumerator: w(x)=1x^0+84x^144+206x^147+206x^150+282x^153+574x^156+1290x^159+1418x^162+1390x^165+508x^168+128x^171+128x^174+98x^177+84x^180+52x^183+52x^186+24x^189+22x^192+6x^195+2x^198+4x^201+2x^225 The gray image is a linear code over GF(3) with n=243, k=8 and d=144. This code was found by Heurico 1.16 in 1.73 seconds.