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 0 1 1 X 1 1 X^2 X 1 1 X^2 1 X 0 0 X 0 X 0 0 X X 0 0 X^2+X X^2+X 0 0 X^2+X X^2+X 0 0 X X^2+X 0 0 X^2+X X^2+X X^2 X X^2+X 0 X^2 X X^2 X^2+X X^2+X X X^2 0 X^2+X X^2 X^2 X^2+X 0 X^2+X X^2 X X^2 0 X X^2+X X^2+X X^2+X X^2 0 X^2 X^2+X X X^2 0 X^2+X X 0 0 X X^2 X X^2+X X^2 X^2 X^2 X X X^2 0 0 X X^2 0 X^2 X X X X X X^2+X X X^2+X 0 X^2 0 0 X X 0 X^2+X X 0 X^2+X 0 X^2+X 0 0 X X^2+X 0 0 X^2+X X 0 0 X X^2+X 0 X X^2+X X^2 X^2 X^2+X X^2+X X^2 0 X X^2 X X^2 0 X^2 X X X X X^2 X^2 0 X X^2 X X^2+X X^2 0 X^2+X X^2 X^2 X X^2+X X^2+X X 0 X^2+X 0 X 0 X^2 X X^2 0 X^2 0 0 X X^2 X X^2 X^2+X X^2 X 0 0 X X^2+X X^2+X X X X^2 X^2+X X 0 0 0 X^2 0 0 X^2 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 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 0 X^2 0 X^2 0 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 0 0 0 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 generates a code of length 87 over Z2[X]/(X^3) who´s minimum homogenous weight is 82. Homogenous weight enumerator: w(x)=1x^0+129x^82+16x^83+60x^84+144x^85+101x^86+208x^87+39x^88+112x^89+91x^90+32x^91+23x^92+55x^94+3x^96+8x^98+1x^100+1x^160 The gray image is a linear code over GF(2) with n=348, k=10 and d=164. This code was found by Heurico 1.16 in 68.9 seconds.