The generator matrix 1 0 1 1 1 0 1 1 0 1 1 X 1 1 0 0 1 1 1 1 0 X 1 1 1 0 1 1 1 1 1 1 0 1 0 0 1 1 1 0 1 0 1 X 1 1 0 1 1 1 1 1 X 1 1 1 1 1 1 1 0 1 X 0 X 0 1 1 0 1 1 0 1 1 0 1 1 X X+1 1 1 0 X+1 0 X+1 1 1 0 X+1 X 1 X+1 X+1 X X+1 0 X+1 1 0 1 1 X+1 X+1 0 1 X 1 X 1 X X 1 1 1 1 1 1 1 X 1 X+1 X X X 1 1 X 1 1 0 0 0 X 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 0 X X X X X X X X X X X X X X X X X 0 X 0 0 X X X X X X 0 X X X 0 0 0 X 0 0 0 0 0 0 0 0 X 0 0 0 0 X 0 X 0 0 X X 0 X 0 X 0 X X 0 X 0 X X 0 X 0 0 0 0 X X X X 0 X 0 0 0 X X X 0 X 0 0 0 X X 0 X 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 X 0 X X X X 0 0 X X X 0 X X X X 0 0 X X 0 0 X 0 X 0 X X 0 X 0 X 0 X 0 X X X 0 0 0 0 X X X X 0 0 0 0 X 0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 0 X X X 0 X 0 X 0 0 X 0 0 X X 0 X 0 X 0 0 X 0 X 0 0 0 X X X 0 0 0 X 0 X X 0 X 0 X X X X 0 X 0 X 0 X 0 0 0 0 0 0 0 X 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 0 X X X X 0 0 X X 0 X 0 X 0 0 0 0 X X X X X 0 0 X 0 X 0 0 X X X X 0 0 0 0 0 0 0 X 0 0 0 0 0 X X 0 X X X 0 0 0 X 0 0 X X X X X 0 0 0 X X 0 X X X X X 0 0 X 0 0 X X 0 X 0 X 0 0 0 0 X X X X 0 X X 0 0 0 0 0 0 0 0 0 0 X 0 0 X 0 0 X 0 0 X X X X 0 0 X X X X 0 X X X 0 X X X 0 0 X X X X X X X X X X 0 X X X 0 0 0 0 X X 0 0 X 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X 0 0 X 0 X X X X 0 0 X 0 0 X X 0 X X 0 X X 0 0 0 X 0 0 X 0 0 X 0 X 0 0 0 X X 0 X 0 0 X X 0 0 0 0 X 0 X X 0 0 X 0 0 0 0 0 0 0 0 0 0 X 0 0 X X X 0 X 0 X X 0 X X 0 0 X X X 0 X X 0 0 X X 0 X X X 0 X 0 0 0 X X X X X X 0 0 X X 0 X 0 0 X X X 0 X X generates a code of length 65 over Z2[X]/(X^2) who´s minimum homogenous weight is 52. Homogenous weight enumerator: w(x)=1x^0+164x^52+66x^54+501x^56+392x^58+942x^60+822x^62+1358x^64+976x^66+1082x^68+606x^70+709x^72+200x^74+250x^76+10x^78+85x^80+26x^84+2x^88 The gray image is a linear code over GF(2) with n=130, k=13 and d=52. This code was found by Heurico 1.16 in 11.8 seconds.