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 1 1 1 1 X X 1 X 1 1 X X 1 X 1 1 X X 1 1 X 1 0 X 0 0 0 0 0 0 0 0 0 0 0 0 X 2X 2X X 2X 2X 2X X 2X 2X X X X 0 X X X 2X 0 0 2X X X 2X 0 2X X 0 2X 2X 2X X 0 2X X X X 0 X X 0 0 X 2X 0 2X 0 X 0 X X 2X 2X 0 X X X X X 2X X X X X 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 X X 2X 2X 2X 2X 2X 2X X 2X 0 X 2X 0 2X 0 X 0 2X 2X 0 0 X X X 2X 0 X 0 2X X 2X X X X X 2X 0 X 0 2X 2X 0 X X 0 2X 0 2X X 0 X 2X 0 0 0 0 0 X 0 0 0 0 X 2X 2X 2X 0 0 X 0 X 2X X 2X 2X 2X 0 X X 0 2X X 0 0 0 X X X 2X 2X 2X 0 X 0 2X 2X 2X 2X 2X 0 X X X X 2X 0 X X X X 0 0 X X 0 2X X 0 2X X 2X 2X 2X 0 X 0 2X 0 2X 2X 2X 0 2X 0 0 0 0 X 0 0 X 2X 0 2X 0 0 2X 2X X X X 2X X 0 2X 2X X 0 0 0 X 0 0 2X X X X 0 0 2X 0 2X 2X 0 2X 0 X 2X 2X 0 2X 2X X 2X 2X 2X 2X 2X 2X X X X 0 0 X 2X 2X 0 X 2X 0 X 0 0 X X 0 X 2X 2X X X 0 0 0 0 0 X 0 2X 2X X 0 2X 2X 2X 2X 2X 2X 0 X 0 0 2X 0 2X X X 2X 2X X 0 0 2X 2X 2X 2X 0 0 2X X 0 0 2X 0 0 X 0 X 2X 2X 0 2X 2X 0 X 0 2X 2X 2X 0 2X X X 2X 2X 0 0 X 2X X X X 0 0 2X 0 2X 0 2X 2X 0 0 0 0 0 0 X 2X 2X 2X 2X 2X 2X X X X 0 2X 0 0 X 0 2X X X X X 2X 0 0 X 2X 0 X 2X 2X X X 2X 2X X 2X X X X 2X 0 2X X X 2X 0 0 X X 0 2X X X 0 2X 2X 2X X 0 2X 0 X X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X generates a code of length 79 over Z3[X]/(X^2) who´s minimum homogenous weight is 141. Homogenous weight enumerator: w(x)=1x^0+152x^141+192x^144+296x^147+486x^150+856x^153+1066x^156+1382x^159+1014x^162+506x^165+196x^168+106x^171+86x^174+70x^177+58x^180+36x^183+32x^186+12x^189+8x^192+4x^195+2x^207 The gray image is a linear code over GF(3) with n=237, k=8 and d=141. This code was found by Heurico 1.16 in 7.22 seconds.