The generator matrix 1 0 0 0 0 0 0 1 1 1 X 0 1 1 0 1 1 X 1 0 1 1 X X 1 0 1 1 X 1 1 1 1 1 X 1 X X 1 1 1 X 0 X 0 X X 1 X 1 1 1 1 X 0 1 1 1 X 1 1 0 X 1 0 0 X X X X 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X 0 0 X X X X X 0 0 X X 0 0 0 X 1 1 1 1 1 1 1 1 1 1 1 1 X+1 1 1 X+1 X+1 1 1 1 X 1 1 1 0 X+1 1 1 X X X 1 0 0 1 X+1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 X+1 1 X X+1 1 1 X 0 X+1 X+1 X 0 1 0 1 0 1 X X+1 X+1 X+1 X X+1 X 1 X+1 X 0 X X+1 1 X+1 0 X+1 1 X X+1 1 1 X+1 0 X+1 0 1 1 0 1 X X X 1 X X 0 0 0 0 1 0 0 0 0 0 0 0 X 0 0 0 X X X X X 1 X+1 X+1 X+1 1 1 X+1 1 1 1 1 X+1 1 X+1 1 1 1 0 X X X+1 0 X+1 X 1 X+1 0 X 0 X+1 X X X+1 X X 0 1 1 1 1 X 0 X+1 X+1 1 0 X 1 1 X X+1 0 0 0 0 0 1 0 0 0 1 1 1 1 0 X X X X+1 1 1 1 1 X+1 0 X 1 1 0 X 0 0 X+1 X+1 X+1 X X 0 X+1 0 X X+1 1 0 1 0 X+1 X 0 1 X+1 X 0 1 1 X+1 1 1 0 0 X+1 0 X X X+1 X+1 0 1 0 X+1 X+1 X X+1 0 0 0 0 0 0 1 0 1 0 X+1 1 1 1 0 X+1 0 0 0 1 1 0 X X X+1 1 X+1 0 1 1 X 1 0 X 1 X+1 0 X+1 1 X X X+1 0 0 X X X X+1 X 0 0 0 X+1 X X X+1 1 X X X+1 X+1 0 0 0 X+1 0 X+1 0 0 1 X+1 0 0 0 0 0 0 0 0 1 1 X+1 X 1 0 X 1 1 0 0 X+1 X+1 0 0 X+1 1 0 1 X X X+1 1 1 0 X 1 0 X 1 X+1 1 X+1 1 0 1 X X X+1 X X 0 X 1 0 X 1 0 X X 0 0 1 X+1 X+1 0 X X 0 X+1 1 1 1 X+1 0 1 0 0 0 0 0 0 0 X X 0 0 X 0 0 X X 0 X 0 0 0 0 0 X X X 0 0 X X X X X 0 0 0 X 0 X 0 0 X X 0 0 X 0 X X X X 0 0 0 X X X 0 X X X 0 0 X 0 X 0 X 0 0 X 0 generates a code of length 72 over Z2[X]/(X^2) who´s minimum homogenous weight is 57. Homogenous weight enumerator: w(x)=1x^0+36x^57+146x^58+224x^59+387x^60+526x^61+631x^62+796x^63+1036x^64+1182x^65+1400x^66+1540x^67+1556x^68+1818x^69+1897x^70+2048x^71+2067x^72+1974x^73+1985x^74+2014x^75+1797x^76+1566x^77+1440x^78+1212x^79+1005x^80+710x^81+565x^82+408x^83+284x^84+210x^85+110x^86+72x^87+51x^88+34x^89+15x^90+6x^91+8x^92+8x^93+1x^94+1x^98+1x^118 The gray image is a linear code over GF(2) with n=144, k=15 and d=57. This code was found by Heurico 1.11 in 60.4 seconds.