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 X X^2 1 1 1 1 1 X 1 1 X 1 0 1 X 1 0 1 0 X^2 1 X 1 0 X^2 1 X X^2 X X 0 X 0 X 0 0 X X^2+X 0 X^2 X X^2+X 0 X^2+X X^2 X^2+X X 0 X^2 X X^2 X^2+X 0 X^2+X 0 X^2 X^2 X X 0 X X 0 X^2 X X^2+X 0 X^2 0 0 X X X^2+X X X^2+X X^2+X X 0 X^2 X X^2 0 X^2+X X^2 0 X^2+X X^2+X X 0 X^2 X X^2 X^2+X X^2+X X X^2 X X X X 0 0 0 0 X X 0 X^2+X X 0 X^2 X X 0 X^2 X^2+X X X^2 X 0 X^2+X 0 0 X^2 X^2+X X 0 0 X X X^2 X^2+X X^2+X X^2 0 X X 0 0 X^2+X X^2+X X^2 X X^2 X^2 X^2+X X^2 0 X^2 X X^2 X X^2 X^2 0 X^2+X X X^2 X^2 0 X X X^2 X X^2 X X^2 X 0 X^2 X^2+X X X^2+X 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 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 X^2 X^2 0 0 0 X^2 0 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 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 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 generates a code of length 72 over Z2[X]/(X^3) who´s minimum homogenous weight is 64. Homogenous weight enumerator: w(x)=1x^0+78x^64+160x^66+253x^68+400x^70+380x^72+313x^74+232x^76+106x^78+56x^80+36x^82+19x^84+6x^86+4x^88+3x^90+1x^112 The gray image is a linear code over GF(2) with n=288, k=11 and d=128. This code was found by Heurico 1.16 in 0.58 seconds.