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 X X^2 X X^2 X X X 0 1 X X 1 1 0 X^2 1 X^2 1 1 X X^2 X 0 1 1 0 1 X X^2 1 0 X 0 0 0 0 0 0 0 X^2+X X X X X X^2 X^2 0 X X^2 X^2+X X 0 X^2 X^2 X 0 X X^2+X X^2 X^2+X 0 X X^2+X X^2+X X^2 X^2 X X^2 X X X^2+X X^2 X^2+X X X 0 X^2+X X X^2 X^2 X^2 X^2+X X^2 X^2 0 X X X 0 0 X^2+X X^2 X X^2 0 X^2+X 0 0 X 0 0 0 X X^2+X X X^2 X X^2+X 0 0 X X^2+X X^2+X X^2+X 0 X^2 X X^2+X X^2+X X^2+X X X^2 X^2+X X X^2+X 0 0 X^2 X X^2+X 0 X^2 X^2+X X X^2 0 X^2 X 0 0 X X^2 X^2+X 0 X^2+X 0 X X X 0 X X^2 X^2+X X^2 X X^2 X^2+X X X^2 X X 0 0 0 0 X 0 X X X 0 X^2+X X^2 X X^2+X 0 X X^2+X 0 0 X^2+X X X^2 X X^2 0 X^2 0 X X 0 X 0 0 X^2 X^2+X X^2 X^2+X X^2+X 0 0 X^2 0 X^2 0 X^2 X X X X^2 X X 0 X X^2 X^2 X^2+X 0 X^2 X X X 0 X^2 X X^2 X^2 X 0 0 0 0 X X 0 X X^2+X X 0 X X^2 X^2+X X^2+X 0 X X^2+X X^2 X^2 0 X^2+X 0 X 0 X X^2+X 0 X^2 X^2+X X^2 X^2 X X^2+X 0 X^2+X X^2+X X X^2+X X X^2 X^2 X^2 X^2 0 X X^2+X X^2+X X X^2 0 X^2+X 0 X 0 X^2+X X X^2+X X 0 X^2+X X^2+X 0 0 X^2+X X^2+X 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 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 X^2 0 X^2 X^2 X^2 X^2 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 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 generates a code of length 66 over Z2[X]/(X^3) who´s minimum homogenous weight is 56. Homogenous weight enumerator: w(x)=1x^0+113x^56+8x^57+370x^58+48x^59+552x^60+176x^61+712x^62+300x^63+901x^64+464x^65+982x^66+508x^67+918x^68+336x^69+604x^70+164x^71+453x^72+40x^73+276x^74+4x^75+165x^76+58x^78+28x^80+4x^82+4x^84+2x^86+1x^92 The gray image is a linear code over GF(2) with n=264, k=13 and d=112. This code was found by Heurico 1.16 in 5.79 seconds.