The generator matrix 1 0 0 0 1 1 1 0 1 1 1 1 X X X 1 0 X 0 X 1 0 X 1 1 1 X X X X 1 1 1 X 1 1 X 0 0 1 1 1 1 1 X 1 0 1 X 1 1 0 0 1 0 X 1 1 X X 0 X 0 0 1 1 X 1 X 1 1 0 1 1 1 X 1 1 1 X 1 1 1 0 0 1 0 0 0 1 1 1 0 X X+1 X+1 1 1 X 0 0 0 1 1 0 1 1 1 1 X 0 0 1 1 X X X+1 1 X+1 X+1 1 X 0 0 X+1 X 0 0 0 X 0 X+1 X X X+1 1 1 X+1 0 1 X+1 X 1 1 X 1 1 0 0 1 1 X+1 X 0 X+1 1 1 0 1 1 X+1 0 0 X 0 1 X 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 X+1 0 1 0 X X+1 1 1 1 X 0 1 X+1 1 1 1 X X+1 0 X 1 0 1 X X X X 0 X X+1 1 1 1 0 X+1 X 1 X X X X+1 0 X 0 1 X+1 1 X 1 X X+1 X+1 0 X 0 1 X X X+1 1 0 0 0 1 1 0 1 1 1 0 X+1 X 1 X 1 X+1 0 1 0 X 0 X+1 1 X X 0 1 1 1 1 X 0 1 X X+1 0 1 X X 1 X+1 1 X X+1 0 0 1 1 1 X 0 0 X+1 1 X+1 1 X+1 X X+1 X+1 X+1 X+1 X+1 1 1 1 0 0 1 1 X+1 0 X X X+1 0 0 X X+1 1 0 1 X 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 X X 0 X 0 X X 0 X 0 X X 0 X X X 0 0 0 0 X 0 0 X 0 X X 0 X 0 X X 0 X X 0 X X X 0 X 0 X 0 0 0 0 X X 0 0 X X 0 X 0 X 0 0 0 0 0 0 X 0 0 0 0 0 0 X 0 X X X X X X X X 0 X 0 X 0 0 0 X X 0 0 X X X 0 0 0 X 0 X 0 0 X X X 0 X X 0 0 X X X 0 X 0 0 0 0 0 X X 0 0 X X X X 0 X 0 X 0 0 0 X 0 X 0 X 0 X 0 0 0 0 0 0 X 0 0 0 0 0 0 X 0 X X X 0 X 0 X X 0 X 0 X 0 0 X 0 0 X X X X 0 0 X X X 0 X 0 X X 0 0 X 0 X X X 0 0 X 0 0 X 0 0 X X 0 X 0 0 0 X 0 0 X 0 X 0 X 0 0 0 X 0 0 X 0 0 0 0 0 0 0 0 X 0 0 X 0 X X 0 X X 0 0 0 0 0 X 0 0 X 0 X 0 X X X X 0 X X X 0 0 X 0 0 X X X 0 0 X X 0 0 0 0 0 X 0 0 X X X X 0 X X X 0 X 0 X 0 X X 0 X 0 0 X 0 0 0 X 0 X 0 0 0 0 0 0 0 0 0 X X X X X X X X 0 0 0 X X X 0 X X X 0 X 0 X 0 0 X 0 0 X X X X X 0 0 X 0 X 0 X 0 X 0 X X 0 X X 0 0 X 0 0 0 0 0 0 0 0 X 0 0 0 0 0 X X 0 X 0 X X X 0 0 0 0 generates a code of length 84 over Z2[X]/(X^2) who´s minimum homogenous weight is 72. Homogenous weight enumerator: w(x)=1x^0+218x^72+394x^74+714x^76+656x^78+975x^80+704x^82+977x^84+818x^86+869x^88+586x^90+565x^92+340x^94+228x^96+76x^98+43x^100+10x^102+13x^104+5x^108 The gray image is a linear code over GF(2) with n=168, k=13 and d=72. This code was found by Heurico 1.16 in 17.8 seconds.