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 X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 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 X X X X X X X X X X X X X X X X X X X X X 0 0 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 0 0 X X X 0 X X 0 0 X X X 0 0 X 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 0 X 0 X X 0 X X 0 X 0 X 0 0 0 X X 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 X X X X 0 X X 0 X X 0 X X 0 0 0 X X 0 X X X 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 X 0 X 0 0 X X X 0 X X 0 X 0 0 0 0 X 0 X 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 X 0 0 0 X X X 0 X 0 X 0 X X X X X 0 X 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 0 X 0 0 0 X X X X 0 X 0 X 0 0 X 0 X 0 X X 0 0 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 X 0 0 X 0 X 0 X X 0 0 X X 0 X X X 0 X 0 0 X 0 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 X 0 X X 0 0 X X X X 0 0 X 0 0 X X 0 0 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 0 X X X X 0 X 0 X X 0 X X 0 X 0 X 0 0 X 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 X X 0 0 0 X 0 X X X 0 X 0 X X 0 X X X X 0 X 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+171x^40+483x^44+631x^48+1779x^52+2048x^54+1791x^56+657x^60+460x^64+153x^68+17x^72+1x^104 The gray image is a linear code over GF(2) with n=108, k=13 and d=40. This code was found by Heurico 1.16 in 22.2 seconds.