The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X 1 X X 1 X X X X X 1 1 0 X 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X X X X X X X 0 X X 0 X X 0 X 0 X X 0 X X X 0 0 0 X 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 X X X X X X X 0 0 X 0 0 X 0 0 X X 0 X 0 0 0 X X X X X 0 0 X 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X 0 0 0 X X X X X X 0 0 0 0 X X 0 X 0 0 X X 0 0 0 0 X X X X X 0 X 0 0 0 X 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 X 0 X X X X X X 0 X X 0 X X X 0 0 0 X 0 0 0 X X 0 0 0 X X X 0 X 0 X X 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 X X 0 X X 0 X 0 X 0 X X X 0 X 0 0 X X 0 0 0 0 X 0 X 0 0 X 0 X X X 0 0 X X 0 0 0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 0 X X X X 0 X X 0 X 0 X 0 X 0 0 X 0 X 0 X 0 0 X X X X 0 X X 0 0 X 0 X 0 0 X X 0 0 0 0 0 0 0 X 0 0 0 X 0 0 0 0 X X 0 X 0 0 0 X X X 0 0 0 X X 0 X 0 X 0 0 X X X X X 0 X X 0 0 X 0 0 X X X X 0 0 0 0 0 0 0 0 X 0 0 X 0 0 0 X 0 0 X 0 X 0 0 X 0 0 0 0 X X X 0 0 X 0 X X X X X X X X 0 X 0 0 X X X X X 0 0 0 0 0 0 0 0 0 0 0 X 0 X X X X X 0 0 0 X 0 0 X X 0 0 X 0 X X 0 X X X 0 0 X 0 0 X 0 0 X 0 X X 0 X X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X 0 0 X X X X X 0 X 0 X 0 0 0 0 0 0 0 0 0 0 X X 0 0 X 0 0 X X X X 0 X X X 0 0 0 generates a code of length 54 over Z2[X]/(X^2) who´s minimum homogenous weight is 40. Homogenous weight enumerator: w(x)=1x^0+85x^40+235x^44+20x^46+440x^48+240x^50+768x^52+504x^54+811x^56+240x^58+418x^60+20x^62+215x^64+80x^68+15x^72+3x^76+1x^88 The gray image is a linear code over GF(2) with n=108, k=12 and d=40. This code was found by Heurico 1.16 in 2.98 seconds.