The generator matrix 1 0 1 1 1 X^2+X 1 1 0 1 X^2+X 1 1 1 0 1 1 X^2+X X^2 1 1 1 1 X 1 1 0 1 1 X^2+X 0 1 1 1 1 X^2+X 1 1 0 1 1 X^2+X X^2 1 1 1 1 X X 1 1 X 1 1 X 1 1 1 1 1 1 1 1 1 1 X 1 1 X 1 1 1 1 0 X^2 X 1 1 X 0 1 1 X^2 1 0 X 0 1 X+1 X^2+X 1 1 0 X+1 1 X^2+X 1 X^2+1 X+1 0 1 X^2+X X^2+1 1 1 X^2 X^2+X+1 X X^2+1 1 0 X+1 1 X^2+X X^2+1 1 1 0 X+1 X^2+X X^2+1 1 0 X+1 1 X^2+X X^2+1 1 1 X^2 X^2+X+1 X 1 1 0 0 X^2+X X^2 X^2 X 0 X^2 X^2 X^2+X X X^2 0 X X^2+X X^2+X X^2+X X^2+X X+1 X^2+1 X X^2+X+1 1 X^2 X^2+X+1 1 X 1 X^2 X^2+X+1 1 1 X+1 X X X^2 1 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 0 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 0 0 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 0 0 0 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 generates a code of length 86 over Z2[X]/(X^3) who´s minimum homogenous weight is 81. Homogenous weight enumerator: w(x)=1x^0+80x^81+100x^82+160x^83+85x^84+116x^85+49x^86+88x^87+71x^88+100x^89+47x^90+56x^91+3x^92+20x^93+21x^94+16x^95+4x^97+4x^98+1x^110+1x^114+1x^126 The gray image is a linear code over GF(2) with n=344, k=10 and d=162. This code was found by Heurico 1.16 in 33.2 seconds.