The generator matrix 1 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1 X 1 X 1 0 X X 1 1 X 0 1 0 0 X X 1 1 1 1 0 X 1 1 1 1 0 1 X 1 1 0 X 1 1 X 0 1 1 1 0 1 1 1 1 X 1 1 X 1 X 0 0 1 0 1 0 1 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 1 1 1 1 1 X+1 1 1 X X X X+1 X 1 1 X X X 1 1 X+1 1 X 1 X X+1 X 1 1 X+1 X X+1 1 1 1 X X+1 X 1 1 X 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 X X X X 1 X+1 1 1 1 1 X 1 1 X+1 1 1 X X+1 1 X X+1 X 0 1 1 X+1 X 1 X+1 X+1 1 0 0 X X 0 1 0 X+1 X+1 1 1 X+1 X+1 0 1 X+1 0 1 1 1 X X 0 1 1 X 0 0 0 0 1 0 0 0 0 0 1 1 X+1 1 X+1 0 0 X X 1 X X+1 X+1 X+1 1 1 0 X 0 X+1 0 X 0 0 X+1 1 0 1 0 1 X+1 X X+1 X+1 X+1 0 X 1 X+1 1 X+1 X 0 X 1 1 X+1 X X X 0 X+1 0 1 X 1 X+1 1 X 1 0 0 0 0 0 0 0 1 0 0 0 1 0 X X+1 X+1 X 1 X+1 0 X X+1 0 0 X+1 1 X+1 1 1 1 1 0 X 1 X 1 X+1 X+1 X+1 X X+1 0 X+1 X X 0 0 1 0 1 1 0 X+1 X+1 0 X+1 X+1 X+1 1 X X+1 X+1 X X+1 1 1 1 X 0 X X+1 X+1 1 1 0 0 0 0 0 0 1 0 0 1 X 1 0 1 X X 1 1 X 1 1 X 0 0 X X+1 0 1 0 1 0 0 1 X+1 1 X X X+1 1 X+1 X+1 X+1 1 X+1 0 1 X+1 X X 0 X 0 1 1 0 X+1 0 1 X+1 1 0 X 1 0 1 X+1 X+1 X+1 0 0 X+1 X+1 0 0 0 0 0 0 0 1 0 1 X+1 X X 1 0 1 X X+1 X+1 X 1 0 1 X X+1 X+1 1 1 X X X+1 X+1 1 0 X+1 X 1 1 0 1 0 1 0 X X X 0 X+1 X+1 X X X X 1 X+1 X+1 0 X X X+1 X 0 0 1 1 X+1 X+1 X X+1 X 1 1 0 0 0 0 0 0 0 0 1 X X 0 X X 1 1 1 1 1 X+1 0 1 1 X 0 X 0 X+1 0 1 1 0 X X 1 X+1 X X X+1 X+1 X+1 X+1 0 1 X+1 0 1 X X+1 0 1 1 1 X 1 X 1 X+1 X+1 0 X 0 X+1 X 1 0 0 X+1 X X+1 X+1 0 0 generates a code of length 72 over Z2[X]/(X^2) who´s minimum homogenous weight is 56. Homogenous weight enumerator: w(x)=1x^0+108x^56+144x^57+413x^58+520x^59+805x^60+956x^61+1277x^62+1474x^63+1916x^64+2256x^65+2569x^66+3020x^67+3260x^68+3526x^69+3886x^70+4154x^71+4066x^72+4466x^73+4014x^74+3984x^75+3395x^76+3228x^77+2789x^78+2260x^79+1900x^80+1364x^81+1179x^82+796x^83+618x^84+360x^85+324x^86+154x^87+158x^88+74x^89+47x^90+16x^91+26x^92+8x^93+12x^94+6x^95+3x^96+2x^98+2x^101 The gray image is a linear code over GF(2) with n=144, k=16 and d=56. This code was found by Heurico 1.11 in 264 seconds.