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 1 1 1 1 1 1 X 1 1 1 1 0 1 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 0 X^2 X X^2+X X^2 0 X X^2+X X^2 X^2+X X^2+X X^2 X^2+X X^2 X X^2 X^2+X X 0 0 X X^2 X^2 X^2+X 0 X X^2 X^2+X X^2+X X^2 X^2 X^2+X X^2+X 0 X^2 0 X^2+X X^2+X X^2 X^2+X X X^2+X X^2 X^2 X X X^2 X^2+X 0 X X^2+X X X X^2 X^2+X X X^2 X X^2 X^2+X X X X X^2 0 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^2 X X 0 X X^2 X^2+X X^2 X^2+X X^2 X^2+X 0 X^2 0 X X^2+X X X^2 X X^2 0 X^2+X X^2 X X X^2+X X^2 X^2 0 X X^2 X X X^2 X^2+X X^2+X 0 0 X^2 X X^2+X X^2 X^2+X X X X^2 X X X^2+X X^2 0 X^2+X X X^2+X X^2+X 0 X X^2+X 0 X^2 X 0 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 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 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 0 X^2 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 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 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 generates a code of length 89 over Z2[X]/(X^3) who´s minimum homogenous weight is 84. Homogenous weight enumerator: w(x)=1x^0+140x^84+96x^87+162x^88+320x^89+96x^91+147x^92+61x^96+1x^172 The gray image is a linear code over GF(2) with n=356, k=10 and d=168. This code was found by Heurico 1.16 in 3.07 seconds.