The generator matrix 1 0 0 0 1 1 1 0 1 1 1 0 X X 1 1 X X X 1 1 1 1 1 0 X 1 0 0 X 0 0 1 0 0 1 1 1 1 0 1 0 0 1 1 1 1 X 1 1 X X 1 X 0 0 X X 0 1 0 1 1 1 X X 1 0 0 X 1 X 1 X X 0 0 1 1 1 X 0 0 1 0 0 0 1 1 1 X 0 X+1 1 1 0 1 1 1 X 1 X X+1 0 X+1 X 0 1 X+1 1 1 1 X X 0 1 1 X+1 1 0 X X X+1 X X 1 1 X+1 X+1 1 X+1 X 1 1 1 1 0 1 1 1 1 0 1 X+1 X 1 0 0 1 X 1 1 X+1 0 0 0 1 1 1 0 0 X+1 1 1 0 0 1 0 1 1 0 1 0 X+1 X 0 1 1 X X+1 0 X 1 X+1 X 1 X+1 X 1 X+1 X+1 0 X 0 1 1 1 X+1 0 0 0 X X 1 X+1 X 1 0 X+1 1 X X+1 0 1 0 1 X+1 X+1 0 X X X+1 1 X+1 0 X+1 X+1 1 1 1 X 1 0 0 0 X 1 X X X+1 X+1 0 X X 0 X+1 0 0 0 1 1 0 1 1 1 0 X X+1 0 X+1 0 X+1 1 1 X 0 1 X+1 X+1 X+1 X X+1 0 X X 1 1 1 X+1 1 1 1 X X X X 1 1 1 X+1 X+1 1 0 X 1 X X 1 0 X+1 1 1 X+1 X+1 0 X+1 1 X X X+1 1 1 1 1 0 X X 1 0 1 1 0 X+1 X X+1 0 X 1 0 0 0 0 X 0 0 0 0 X 0 0 0 X 0 X X X 0 X X 0 0 X 0 0 0 X X X X 0 X X 0 X X X 0 0 X 0 X 0 0 X 0 0 0 X X X X 0 0 X X X 0 0 0 X X X 0 0 0 X X 0 0 X X X 0 0 0 X X 0 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 0 0 0 X X X X X X X X X X X X 0 0 X X 0 X X 0 X 0 0 X X 0 0 X 0 X 0 X X 0 X X 0 0 X 0 X X 0 0 X X 0 0 0 X X X X 0 X 0 0 0 0 0 0 0 X 0 0 0 X X X X 0 0 0 X 0 X 0 X 0 0 X X X X 0 0 X 0 0 X 0 0 0 X X 0 X 0 0 0 X 0 0 X X X 0 X 0 0 X 0 X 0 0 X X 0 X X X 0 0 0 0 0 X X 0 0 X X X 0 0 X X 0 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 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 X X X X X X 0 X X 0 0 0 0 X X X 0 X X X X X 0 0 X 0 X 0 generates a code of length 82 over Z2[X]/(X^2) who´s minimum homogenous weight is 72. Homogenous weight enumerator: w(x)=1x^0+204x^72+360x^74+510x^76+440x^78+436x^80+388x^82+464x^84+376x^86+305x^88+224x^90+178x^92+96x^94+69x^96+36x^98+8x^100+1x^104 The gray image is a linear code over GF(2) with n=164, k=12 and d=72. This code was found by Heurico 1.16 in 5.06 seconds.