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 1 1 1 1 1 1 1 1 1 1 1 1 1 X^2 1 1 1 1 1 1 X X 0 X 2X 0 2X^2+X 2X X^2 X^2+2X 2X^2+X 2X^2+X 0 2X X^2 2X^2+X 2X X^2+2X 0 X^2 2X^2+X X^2+X 2X X^2+2X 2X^2+2X X^2+2X X^2+X 2X^2+X X^2+X X^2 X^2+X 2X^2 X^2+X 2X^2+X X^2+X 2X^2+X X^2+X X^2+X X 2X 2X X^2+2X 2X^2+X 2X X^2+2X X^2+2X 2X^2+2X 0 0 0 X^2 X^2 2X^2 2X^2 0 0 2X^2 X^2+X 2X^2+2X 2X X^2+2X 2X X^2 2X X^2 0 0 2X^2+2X X^2+2X 2X^2+2X X^2+2X X^2+2X X^2 X^2 X^2 2X^2 2X^2+X X^2 2X^2+X X^2+X 2X^2+X X^2+X X^2+X X 0 2X^2+X 0 0 X^2 0 0 0 0 2X^2 2X^2 X^2 X^2 X^2 2X^2 X^2 0 X^2 X^2 2X^2 2X^2 2X^2 2X^2 2X^2 0 X^2 0 X^2 0 X^2 X^2 2X^2 2X^2 2X^2 2X^2 X^2 0 0 X^2 0 0 X^2 2X^2 X^2 X^2 0 0 0 2X^2 X^2 2X^2 2X^2 2X^2 2X^2 X^2 0 X^2 2X^2 2X^2 2X^2 0 X^2 0 X^2 X^2 X^2 0 2X^2 2X^2 2X^2 2X^2 0 0 2X^2 X^2 0 2X^2 0 X^2 0 X^2 2X^2 X^2 X^2 2X^2 2X^2 0 0 0 X^2 0 0 2X^2 0 0 0 0 0 X^2 2X^2 2X^2 X^2 2X^2 2X^2 X^2 2X^2 2X^2 X^2 X^2 2X^2 2X^2 2X^2 X^2 X^2 X^2 0 X^2 2X^2 0 0 X^2 2X^2 X^2 0 2X^2 2X^2 2X^2 2X^2 0 2X^2 0 0 2X^2 0 2X^2 0 X^2 0 2X^2 0 0 2X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 2X^2 X^2 2X^2 X^2 2X^2 X^2 2X^2 2X^2 X^2 0 0 2X^2 X^2 0 0 X^2 0 2X^2 0 0 0 0 2X^2 2X^2 0 X^2 2X^2 X^2 X^2 2X^2 2X^2 0 2X^2 0 X^2 2X^2 2X^2 2X^2 X^2 X^2 2X^2 0 0 X^2 0 X^2 X^2 2X^2 X^2 X^2 X^2 0 2X^2 2X^2 0 0 X^2 X^2 0 2X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 2X^2 2X^2 2X^2 0 0 0 0 X^2 X^2 2X^2 2X^2 0 2X^2 2X^2 0 2X^2 2X^2 X^2 2X^2 0 0 X^2 0 0 2X^2 X^2 2X^2 0 2X^2 2X^2 2X^2 2X^2 generates a code of length 84 over Z3[X]/(X^3) who´s minimum homogenous weight is 161. Homogenous weight enumerator: w(x)=1x^0+336x^161+114x^162+846x^164+342x^165+972x^167+216x^168+2916x^169+324x^170+18x^171+144x^173+36x^174+126x^179+144x^182+24x^188+2x^243 The gray image is a linear code over GF(3) with n=756, k=8 and d=483. This code was found by Heurico 1.16 in 0.688 seconds.