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 X^2 1 1 1 1 1 1 X X 1 0 X 2X 0 2X^2+X 2X X^2 X^2+2X 2X^2+X X^2+X 2X 0 2X^2 2X^2+X 2X X^2+2X X^2 X^2 X 2X^2+X X^2+2X 2X X^2+2X 2X^2+X 2X^2+2X X 0 X X^2 X 2X^2+X 2X^2+X X^2+X 2X^2+X X X X 2X 2X X^2+2X 2X X^2+2X X^2+2X 2X^2+2X 0 0 X^2 0 X^2 2X^2 X^2 0 2X^2+X 0 X^2 0 X^2 2X 2X^2+2X X^2+2X 2X^2+2X 2X^2+X X X X^2+X 2X^2+X 2X^2 X^2 X^2 0 2X^2 2X^2 X^2 X^2+X 2X^2+X 2X X^2+2X X 2X^2+2X 2X^2+X 2X^2+X 0 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 2X^2 X^2 0 X^2 0 X^2 2X^2 X^2 2X^2 2X^2 X^2 2X^2 2X^2 0 2X^2 2X^2 0 X^2 2X^2 X^2 0 0 0 2X^2 2X^2 2X^2 X^2 2X^2 0 0 X^2 X^2 X^2 0 0 X^2 2X^2 2X^2 X^2 2X^2 2X^2 X^2 2X^2 0 X^2 2X^2 0 X^2 0 X^2 2X^2 2X^2 X^2 2X^2 0 0 0 0 X^2 X^2 2X^2 X^2 X^2 2X^2 2X^2 2X^2 0 0 0 X^2 0 X^2 2X^2 2X^2 X^2 2X^2 0 X^2 X^2 X^2 0 X^2 2X^2 0 X^2 X^2 2X^2 2X^2 X^2 0 0 2X^2 2X^2 0 0 2X^2 2X^2 X^2 X^2 0 0 2X^2 2X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 2X^2 2X^2 0 0 X^2 0 X^2 0 X^2 2X^2 X^2 0 2X^2 2X^2 X^2 0 X^2 X^2 2X^2 X^2 0 X^2 X^2 2X^2 2X^2 2X^2 0 0 0 2X^2 2X^2 0 2X^2 2X^2 0 0 0 0 0 0 2X^2 2X^2 0 X^2 X^2 0 X^2 X^2 2X^2 X^2 2X^2 0 2X^2 X^2 2X^2 0 2X^2 0 X^2 0 X^2 X^2 X^2 X^2 2X^2 2X^2 2X^2 2X^2 0 X^2 2X^2 X^2 0 X^2 X^2 2X^2 0 2X^2 X^2 0 X^2 2X^2 2X^2 0 2X^2 2X^2 X^2 0 0 X^2 0 0 0 2X^2 0 X^2 2X^2 0 X^2 X^2 X^2 2X^2 0 X^2 2X^2 X^2 X^2 2X^2 0 X^2 2X^2 2X^2 2X^2 0 X^2 2X^2 0 2X^2 generates a code of length 82 over Z3[X]/(X^3) who´s minimum homogenous weight is 156. Homogenous weight enumerator: w(x)=1x^0+142x^156+84x^157+216x^158+290x^159+186x^160+864x^161+236x^162+864x^164+3084x^165+30x^166+86x^168+78x^169+102x^171+96x^174+48x^175+38x^177+60x^178+48x^180+6x^183+2x^237 The gray image is a linear code over GF(3) with n=738, k=8 and d=468. This code was found by Heurico 1.16 in 0.622 seconds.