The generator matrix 1 0 0 0 0 1 1 1 0 1 1 1 0 1 1 X 0 1 1 1 1 1 0 X 0 0 X 1 1 X 1 1 0 X X X 1 1 1 1 X 1 1 X 1 0 1 X 0 1 1 0 X 1 0 1 0 0 0 0 0 0 0 1 X+1 1 1 X+1 X+1 1 1 X 1 1 X 0 1 1 1 0 X 1 X X 0 1 1 0 X 1 0 X+1 X 1 1 0 X 0 0 1 X+1 0 X 1 X+1 1 0 0 0 0 1 0 0 0 1 1 1 1 1 1 1 0 0 1 X 0 X+1 X 1 X X+1 1 X 1 0 X+1 1 1 1 0 X 0 1 X+1 X X X+1 X 1 X X+1 1 0 X X+1 0 X 0 0 X+1 0 0 0 0 0 1 0 1 1 0 1 0 0 1 X+1 1 X X X X X+1 0 0 1 X+1 X X+1 1 1 0 1 X X X+1 X+1 0 1 1 0 X+1 0 0 X 1 X+1 X+1 1 X+1 X+1 X 1 X+1 0 X+1 0 0 0 0 0 0 1 1 0 1 1 0 1 1 0 X+1 1 0 X+1 X+1 0 0 X X X+1 X+1 1 0 X+1 1 1 X+1 X+1 X X 1 1 X+1 X X+1 X 0 X+1 X 1 X+1 X X+1 X 1 X 1 X+1 1 X 0 0 0 0 0 0 X 0 0 0 0 0 0 0 X X X 0 X X 0 X X X 0 X 0 X 0 X 0 0 0 X 0 0 0 X X X X X 0 X X 0 0 0 X 0 0 X 0 X 0 0 0 0 0 0 0 X 0 0 0 0 X X X 0 0 0 X 0 0 X X 0 X X X 0 X X X 0 0 0 X X X X 0 0 X 0 X X X 0 0 0 X 0 X 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 X X X X X X X 0 0 X X 0 X X X X 0 0 0 X 0 0 X 0 X X 0 0 X X 0 X 0 0 0 0 0 0 0 0 0 X 0 X X 0 0 0 X 0 X 0 X X X X X X 0 0 0 X 0 X X X X 0 X 0 X 0 X 0 0 0 X 0 0 X X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X X 0 X X 0 0 X X X 0 0 X X X X 0 0 X X 0 X 0 X 0 0 X X 0 X X X X X 0 0 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+82x^40+86x^41+254x^42+326x^43+555x^44+604x^45+934x^46+1116x^47+1341x^48+1480x^49+1695x^50+2036x^51+2061x^52+2408x^53+2358x^54+2508x^55+2211x^56+2282x^57+1859x^58+1550x^59+1377x^60+1068x^61+842x^62+580x^63+442x^64+228x^65+221x^66+72x^67+99x^68+32x^69+26x^70+4x^71+19x^72+4x^73+3x^74+4x^76 The gray image is a linear code over GF(2) with n=108, k=15 and d=40. This code was found by Heurico 1.16 in 99.9 seconds.