The generator matrix 1 0 0 0 1 1 1 0 1 1 1 1 X X X 1 0 X 0 1 0 1 1 1 X 0 0 1 1 X 1 1 1 1 0 1 1 0 1 1 0 1 1 X 0 0 0 1 1 X X 0 X 0 1 1 X 1 X X 0 1 1 0 1 1 0 0 1 0 0 0 1 1 1 0 X X+1 X+1 1 1 X 0 0 0 1 X 1 X+1 1 1 0 0 1 0 X 1 X+1 X X 1 1 X 0 X 0 X 1 0 X+1 0 X 1 0 1 X+1 1 1 0 1 1 X+1 1 1 X 0 X 1 X+1 0 1 X+1 1 1 0 0 1 0 1 1 0 1 0 1 1 X 0 1 1 X 1 X X 1 1 X+1 0 1 1 1 0 0 1 X+1 X 0 0 1 X X+1 1 1 0 0 X X+1 X 1 0 X+1 X X 1 0 X 0 0 X+1 X X+1 1 X+1 1 X X X X 0 1 1 0 0 0 0 1 1 0 1 1 1 0 X+1 X 1 X 1 X+1 0 1 0 X+1 0 0 1 X+1 0 X 1 X 0 X+1 X 1 0 0 1 0 X X+1 X X X X X 1 1 0 1 1 1 X X+1 1 1 X+1 1 0 X+1 X+1 X+1 1 X+1 X X+1 X 1 1 X 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X X 0 0 X 0 X X 0 0 X 0 0 X X X X X X 0 X 0 0 X X 0 X 0 0 X X X X X X X 0 0 0 X 0 0 X 0 0 0 0 0 X 0 0 0 0 0 0 X 0 X X X X X X X 0 0 0 X 0 0 X X X 0 0 0 X 0 X X X 0 X X X X 0 X 0 0 0 X X X 0 0 0 0 0 0 X 0 0 X 0 X 0 X X 0 0 0 0 0 0 0 X 0 0 0 0 0 0 X 0 X X X 0 X X 0 0 X 0 X X 0 0 X 0 0 0 X X 0 0 0 X 0 0 X 0 X X X 0 0 0 X X 0 0 X X X X X 0 X X 0 0 0 0 0 X 0 0 0 0 0 0 0 X 0 0 X 0 X X 0 X X 0 0 X X X X 0 0 X X 0 X X X X X X 0 X 0 0 X 0 X 0 X 0 X 0 0 0 0 X 0 X 0 X 0 0 X X X 0 X X X 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X X 0 0 0 0 X 0 0 X 0 0 X 0 X 0 X X 0 0 X X X X 0 0 0 X X 0 0 0 X X 0 X 0 X X X 0 X 0 X X X X X X X X 0 X generates a code of length 67 over Z2[X]/(X^2) who´s minimum homogenous weight is 56. Homogenous weight enumerator: w(x)=1x^0+198x^56+464x^58+775x^60+808x^62+944x^64+914x^66+1014x^68+896x^70+888x^72+564x^74+424x^76+168x^78+95x^80+26x^82+10x^84+1x^88+1x^92+1x^104 The gray image is a linear code over GF(2) with n=134, k=13 and d=56. This code was found by Heurico 1.16 in 11.6 seconds.