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 0 1 1 1 1 X 1 0 X 1 1 0 X 0 X 0 0 X X X^2 X^2 X X X^2 X^2+X 0 X^2+X X^2 0 X^2+X X 0 X^2+X 0 X 0 X^2+X X^2 X 0 X^2+X X^2 X X 0 X^2 X^2+X 0 0 X X^2+X X^2 X^2+X X^2 X 0 X^2 X X X 0 X^2+X X^2 X^2+X X X^2 0 0 X^2+X X^2+X X^2+X X^2 X^2 0 X X^2 X^2+X 0 X 0 X X^2 X X 0 X^2+X X^2 0 X^2+X X^2+X X X^2+X X^2+X X X^2+X X X^2 0 0 X X 0 X^2+X X 0 X X^2 X X^2 X^2+X X 0 0 X 0 X X^2 0 X^2 X^2+X X X^2 0 X X^2+X X^2+X X^2 0 X X^2+X 0 X X^2 X^2 X^2+X X^2+X 0 X^2+X X 0 0 X X^2 0 X X^2+X X^2 0 X^2 X^2+X 0 X 0 X X X^2 X^2+X X^2+X 0 X X^2 X^2+X X^2 0 X X^2+X X^2+X X^2 X^2 X^2 X 0 X X^2 X^2+X X X^2+X X^2 X^2+X 0 X^2 X^2+X X 0 0 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 0 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 0 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 0 0 0 0 X^2 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 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 generates a code of length 86 over Z2[X]/(X^3) who´s minimum homogenous weight is 80. Homogenous weight enumerator: w(x)=1x^0+66x^80+89x^82+16x^83+143x^84+112x^85+187x^86+112x^87+146x^88+16x^89+57x^90+56x^92+17x^94+3x^96+2x^98+1x^164 The gray image is a linear code over GF(2) with n=344, k=10 and d=160. This code was found by Heurico 1.16 in 0.559 seconds.