The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 0 X 0 1 1 1 X 1 1 1 0 1 X 0 1 1 X 1 0 X 1 1 0 1 1 1 1 1 0 1 1 1 X 0 1 0 X^2 X 1 0 X 1 X^2 X 1 1 X 1 1 1 1 0 X 0 X^2+X 0 X^2+X 0 X^2+X 0 X^2+X 0 X^2+X X^2+X 0 X^2+X 0 X^2+X 0 X^2+X 0 X^2+X X X^2+X X X^2 X^2 X^2+X X^2+X X^2+X X^2+X X^2 X X X^2+X X 0 X^2 X^2+X 0 X X^2+X 0 X^2+X X X 0 X X^2 0 X 0 X^2+X X^2 X^2+X X X X X^2 X^2+X X X X X 0 0 0 X 0 X^2+X 0 0 0 0 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 X^2 X^2 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 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^2 0 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 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 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 0 X^2 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 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 0 0 X^2 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 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 0 0 0 0 X^2 0 X^2 X^2 0 0 0 X^2 0 0 0 X^2 0 0 0 0 X^2 0 0 0 0 X^2 X^2 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 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 0 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 generates a code of length 72 over Z2[X]/(X^3) who´s minimum homogenous weight is 56. Homogenous weight enumerator: w(x)=1x^0+64x^56+47x^58+18x^59+154x^60+70x^61+204x^62+158x^63+375x^64+394x^65+498x^66+712x^67+860x^68+1184x^69+1232x^70+1596x^71+1385x^72+1492x^73+1199x^74+1186x^75+866x^76+774x^77+566x^78+358x^79+255x^80+162x^81+195x^82+68x^83+96x^84+20x^85+100x^86+31x^88+42x^90+8x^92+10x^94+1x^96+3x^98 The gray image is a linear code over GF(2) with n=288, k=14 and d=112. This code was found by Heurico 1.16 in 26 seconds.