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 1 1 1 1 X 1 X X X 1 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 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 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 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 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 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 0 0 X^2 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 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 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 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 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 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 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 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 0 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 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 0 0 X^2 0 0 0 0 0 X^2 0 0 0 0 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 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 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 0 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 X^2 0 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 0 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 X^2 0 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 0 0 0 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 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 generates a code of length 74 over Z2[X]/(X^3) who´s minimum homogenous weight is 56. Homogenous weight enumerator: w(x)=1x^0+86x^56+58x^58+187x^60+144x^62+306x^64+215x^66+32x^67+303x^68+224x^69+284x^70+672x^71+305x^72+1120x^73+8504x^74+1120x^75+329x^76+672x^77+312x^78+224x^79+235x^80+32x^81+310x^82+181x^84+242x^86+85x^88+126x^90+24x^92+40x^94+6x^96+3x^98+1x^102+1x^134 The gray image is a linear code over GF(2) with n=296, k=14 and d=112. This code was found by Heurico 1.16 in 30.4 seconds.