The generator matrix 1 0 0 0 0 0 0 1 1 1 X 0 1 1 0 1 1 X 1 X X 1 1 0 X 1 X 1 X X 1 0 0 1 0 1 1 X 0 1 1 1 1 1 1 1 1 X 1 1 X 1 1 1 1 1 1 X X X X 0 1 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 X X X X X X X X X 1 X+1 X+1 1 1 X+1 1 X+1 1 1 X+1 X+1 1 1 X+1 X+1 1 1 1 X X+1 X 1 1 X X 1 X 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 X 0 X 1 1 1 0 X 1 X 1 X+1 0 1 X+1 1 0 0 1 X 1 X+1 X+1 0 1 X 1 0 0 X+1 X 0 X X+1 X 1 0 X X X+1 X+1 0 1 0 1 1 X 0 0 0 0 1 0 0 0 0 0 0 0 X 0 0 0 X 1 1 X+1 1 X X+1 X+1 1 X X+1 X X+1 1 1 1 0 X 1 X 0 X X+1 1 X+1 1 X+1 X+1 X+1 X 0 X+1 1 0 0 0 X+1 0 0 1 X 1 X+1 1 X X 1 1 0 0 0 0 0 1 0 0 0 1 1 1 1 0 X X X 0 X+1 X+1 0 X+1 0 X+1 X+1 1 X X+1 X X+1 X 1 0 1 1 0 X 1 1 X X+1 0 1 0 X 0 0 0 X X+1 X+1 X 1 X+1 0 0 X+1 X X+1 X 1 1 1 X+1 0 0 0 0 0 0 1 0 1 0 X+1 1 1 1 0 X+1 0 0 X+1 X X+1 X X+1 X+1 X 1 X+1 0 X+1 X+1 X+1 X X+1 0 X+1 X 0 X+1 X X+1 1 0 X 0 X+1 X X X 1 X+1 X 1 X+1 X X 1 X+1 1 0 1 0 X+1 1 X 0 0 0 0 0 0 0 1 1 X+1 X 1 0 X 1 1 0 0 1 X+1 1 0 X+1 X X+1 X+1 1 X+1 0 X 0 0 0 0 1 1 X+1 0 0 X X+1 X X X+1 1 0 0 0 0 1 X 1 X+1 X 1 X X+1 1 X 0 X+1 X+1 X+1 X+1 0 0 0 0 0 0 0 0 X X 0 0 X 0 0 X X X X 0 0 0 X X X 0 0 X X 0 X X X X X X X 0 X X 0 X 0 X X X 0 X 0 X X X 0 X X X X 0 0 0 0 0 0 X 0 generates a code of length 64 over Z2[X]/(X^2) who´s minimum homogenous weight is 50. Homogenous weight enumerator: w(x)=1x^0+100x^50+170x^51+308x^52+430x^53+632x^54+764x^55+885x^56+1028x^57+1403x^58+1594x^59+1647x^60+2000x^61+2061x^62+2178x^63+2142x^64+2220x^65+2114x^66+1970x^67+1844x^68+1690x^69+1490x^70+1108x^71+849x^72+680x^73+511x^74+340x^75+231x^76+136x^77+121x^78+62x^79+26x^80+8x^81+16x^82+4x^83+2x^84+2x^91+1x^96 The gray image is a linear code over GF(2) with n=128, k=15 and d=50. This code was found by Heurico 1.11 in 55.3 seconds.