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 1 0 1 1 X 0 1 1 1 1 1 0 0 1 1 0 0 X X X 1 0 0 0 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 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 0 1 1 X+1 0 1 0 0 X+1 X X X 0 1 X+1 X 1 1 0 0 0 1 0 0 0 X 0 0 0 0 0 0 0 0 0 X 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 0 0 1 0 1 1 0 1 0 1 0 0 1 X X+1 1 1 1 1 1 X X 0 X+1 1 0 X X+1 0 1 X+1 1 X 0 0 1 1 0 1 1 1 1 0 1 0 1 1 1 1 0 0 0 0 0 0 X 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 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 0 X+1 X 0 0 X X+1 1 0 0 X 0 1 X 1 X 0 0 0 0 0 1 X 0 1 1 0 0 0 0 X 0 0 0 X 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 1 1 1 0 0 1 1 X 1 1 1 X X+1 X+1 1 X X+1 0 0 1 X X X X+1 0 1 0 X X+1 X+1 X+1 0 X+1 X+1 X X+1 1 1 X+1 X+1 0 1 0 0 1 1 1 1 0 X 0 0 0 X 0 0 0 X 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 X 0 0 0 0 0 X 0 X X 0 X 0 X X X 0 X X 0 0 X 0 0 X X 0 X 0 X X 0 0 X X X X X X 0 X X X X X 0 X 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 0 0 0 X 0 0 0 0 X X X 0 0 X X 0 0 X X 0 X 0 0 X X X 0 X 0 X 0 X 0 X 0 0 0 X X 0 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 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 X 0 X 0 X 0 0 X 0 X 0 0 0 0 X 0 0 0 0 0 X X X 0 0 X 0 0 X 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 0 0 0 0 0 0 X 0 X 0 0 X X X 0 0 X X 0 X 0 X 0 0 0 X X 0 0 X 0 X X 0 X X 0 X 0 0 0 X X X 0 0 0 X 0 X X 0 0 X 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 0 0 X 0 X X 0 X X X 0 0 X 0 X X X X 0 0 0 0 X 0 X 0 X 0 0 0 X X X 0 0 0 0 0 0 X X 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 0 0 0 generates a code of length 86 over Z2[X]/(X^2) who´s minimum homogenous weight is 40. Homogenous weight enumerator: w(x)=1x^0+10x^40+28x^42+58x^44+110x^46+189x^48+269x^50+454x^52+649x^54+866x^56+953x^58+1002x^60+940x^62+846x^64+663x^66+470x^68+371x^70+206x^72+257x^74+450x^76+738x^78+1294x^80+1892x^82+2394x^84+2522x^86+2356x^88+2002x^90+1264x^92+764x^94+442x^96+204x^98+253x^100+308x^102+458x^104+717x^106+820x^108+944x^110+1025x^112+985x^114+850x^116+658x^118+416x^120+273x^122+182x^124+103x^126+63x^128+27x^130+11x^132+4x^134+4x^136+2x^138+1x^142 The gray image is a linear code over GF(2) with n=172, k=15 and d=40. This code was found by Heurico 1.16 in 99.7 seconds.