The generator matrix 1 0 0 1 1 1 0 1 1 1 1 0 X X 1 1 1 X 1 1 0 0 X 1 0 0 1 1 1 1 1 1 1 1 1 X X 0 1 X 0 1 0 1 1 1 1 1 1 X X X 1 1 1 1 1 0 1 0 1 0 1 1 0 0 1 X+1 1 X 1 0 1 X 1 X X+1 1 X 1 0 1 1 X+1 0 0 X+1 X 1 1 X X+1 1 1 X X 0 1 1 X X 0 X+1 X+1 X+1 1 1 X 1 X+1 X 1 1 0 0 0 1 1 1 0 1 0 1 1 0 X 1 1 X 1 1 1 X+1 0 0 1 1 0 0 0 X X 1 1 X+1 1 0 X X 1 X+1 1 X+1 1 X+1 X+1 1 X+1 X+1 X X X+1 1 1 1 X X 1 X+1 1 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X 0 X X X X X 0 0 X 0 X X X X 0 X 0 0 0 X X 0 X 0 X 0 0 0 X 0 X 0 0 0 0 0 0 0 X 0 0 0 0 0 X X X 0 0 X 0 X X X X 0 X 0 0 0 0 0 0 X X 0 0 0 0 0 X X X X 0 0 0 0 X X X 0 X 0 X 0 0 X 0 0 0 0 0 0 0 0 X 0 0 0 0 X 0 0 X X X 0 X X 0 X X X 0 0 X 0 0 X 0 0 X X 0 X X 0 0 0 0 X 0 X X X X X 0 0 0 0 X X X X 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 0 X 0 X 0 0 X X X X 0 X 0 X X 0 X 0 0 X 0 X X 0 X 0 X X X X 0 0 X X 0 0 X 0 X 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 X X X X X 0 0 0 X X X 0 0 X 0 X X 0 X 0 0 0 X X 0 X 0 X X 0 X X X 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 X 0 X X X X X 0 X 0 X X 0 X 0 X X 0 X X 0 0 X X 0 X X 0 X 0 0 X 0 X X X 0 X 0 0 0 X X 0 0 X X X 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 0 0 0 X 0 X X X X X 0 X X 0 X 0 X X X 0 X X 0 X X 0 0 X X 0 0 X X X 0 0 X X 0 generates a code of length 57 over Z2[X]/(X^2) who´s minimum homogenous weight is 44. Homogenous weight enumerator: w(x)=1x^0+37x^44+24x^45+86x^46+120x^47+209x^48+214x^49+325x^50+366x^51+397x^52+464x^53+467x^54+582x^55+506x^56+534x^57+573x^58+572x^59+499x^60+568x^61+396x^62+308x^63+284x^64+210x^65+148x^66+86x^67+84x^68+32x^69+43x^70+14x^71+24x^72+2x^73+9x^74+6x^76+1x^82+1x^84 The gray image is a linear code over GF(2) with n=114, k=13 and d=44. This code was found by Heurico 1.16 in 8.37 seconds.