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 X 1 X X X 1 1 1 X X X X X 1 1 1 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 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 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 0 0 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 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 0 0 0 0 X^2 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 0 0 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 X^2 0 0 0 0 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 0 0 0 X^2 0 0 X^2 0 X^2 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 0 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 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 0 0 0 0 X^2 0 X^2 0 0 0 X^2 0 0 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 0 0 0 X^2 0 0 generates a code of length 73 over Z2[X]/(X^3) who´s minimum homogenous weight is 56. Homogenous weight enumerator: w(x)=1x^0+106x^56+345x^60+533x^64+72x^66+873x^68+672x^70+1642x^72+8192x^73+1008x^74+1350x^76+288x^78+636x^80+8x^82+390x^84+204x^88+49x^92+13x^96+1x^100+1x^128 The gray image is a linear code over GF(2) with n=292, k=14 and d=112. This code was found by Heurico 1.16 in 30.2 seconds.