The generator matrix 1 0 0 0 0 1 1 1 1 1 1 1 X X X 0 0 X 0 X X 0 1 0 1 1 1 1 X 0 1 1 1 1 1 0 X X 0 1 X 1 X X X X 0 0 1 1 0 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 0 1 0 0 0 1 0 0 1 1 0 1 1 1 1 1 1 1 0 0 1 X X+1 1 X 0 X+1 X 0 X X+1 X+1 1 1 X+1 X X 0 X 0 1 1 0 0 0 0 0 1 X 0 1 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 0 0 0 0 1 0 0 1 0 1 1 0 1 0 1 0 0 1 X X+1 1 1 1 1 1 0 X 1 1 X+1 X X X+1 X 1 1 X 0 X 1 0 1 X 0 1 0 1 1 X 0 1 1 0 1 0 0 0 0 0 0 0 0 0 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 1 0 1 1 1 0 0 0 1 1 0 0 X+1 X+1 0 X+1 X+1 X+1 1 X 1 0 1 X 0 X 0 X X 0 1 1 1 1 X 0 X X+1 X+1 1 X X X 1 1 0 X+1 1 1 0 0 0 0 0 0 0 0 0 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 1 1 1 0 0 1 1 X 1 1 1 X X+1 X+1 1 X X+1 0 1 X 1 X+1 X 0 1 1 0 0 X+1 X+1 1 X 0 X X X+1 X+1 X X X 1 X+1 0 1 0 X 1 0 0 0 0 0 0 0 0 0 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 X 0 0 0 0 0 X 0 X X 0 X 0 X X X 0 X X X 0 0 X X X 0 X X 0 X X 0 0 0 0 0 0 X 0 0 X 0 X 0 X 0 0 0 0 0 0 0 0 0 0 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 X 0 0 0 0 X X X 0 0 X X 0 0 X X 0 0 X X X X 0 X 0 0 X 0 X X 0 0 0 0 0 X 0 X X X 0 0 0 X X 0 0 0 0 0 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 0 0 X 0 0 X 0 X 0 X 0 X 0 X 0 X X X 0 X X X 0 0 X X X X 0 0 0 0 0 X X 0 X X 0 0 0 0 X X X X X X 0 0 0 0 X 0 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 0 X 0 0 X X X 0 0 X X 0 X 0 X X 0 X 0 X 0 0 0 0 0 X X X X 0 0 0 0 0 X 0 0 X 0 0 X 0 X X 0 X 0 0 0 0 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 0 X 0 X X 0 X X X 0 0 X 0 X 0 X 0 0 X X X 0 0 X X X 0 0 0 X 0 0 X 0 0 X X X 0 0 X 0 X 0 0 0 X 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 generates a code of length 83 over Z2[X]/(X^2) who´s minimum homogenous weight is 40. Homogenous weight enumerator: w(x)=1x^0+5x^40+6x^41+14x^42+18x^43+43x^44+56x^45+68x^46+116x^47+143x^48+158x^49+235x^50+288x^51+315x^52+378x^53+460x^54+442x^55+509x^56+534x^57+534x^58+548x^59+518x^60+552x^61+410x^62+408x^63+325x^64+266x^65+229x^66+184x^67+166x^68+110x^69+136x^70+112x^71+170x^72+246x^73+282x^74+396x^75+519x^76+632x^77+790x^78+964x^79+1037x^80+1134x^81+1264x^82+1290x^83+1305x^84+1166x^85+1094x^86+878x^87+730x^88+696x^89+489x^90+414x^91+315x^92+194x^93+157x^94+148x^95+145x^96+122x^97+157x^98+166x^99+206x^100+270x^101+349x^102+368x^103+433x^104+510x^105+543x^106+586x^107+560x^108+578x^109+455x^110+462x^111+435x^112+348x^113+330x^114+284x^115+213x^116+184x^117+137x^118+100x^119+79x^120+44x^121+50x^122+18x^123+15x^124+8x^125+8x^126+2x^127+4x^128+1x^130+1x^132 The gray image is a linear code over GF(2) with n=166, k=15 and d=40. This code was found by Heurico 1.16 in 99.6 seconds.