The generator matrix 1 0 0 0 0 0 1 1 1 1 1 1 1 0 1 1 0 0 X 1 1 X X X X 0 X 0 1 1 1 1 1 1 1 X 0 0 1 X 1 0 1 1 0 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 0 1 0 0 0 0 1 0 0 X+1 0 1 X X 0 1 1 0 X X+1 X+1 1 0 1 1 0 0 1 1 X X 0 X X+1 0 X 1 1 1 1 X+1 X 0 X X 0 0 0 1 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 1 0 0 0 1 0 1 1 0 X X X 1 0 X 1 X 1 X+1 X 1 X+1 X 1 X 1 1 X X+1 X 1 X+1 X+1 1 0 X 1 X+1 X X 0 X 0 0 X X 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 1 0 0 1 0 1 0 1 X 1 1 X+1 1 0 X+1 1 X+1 1 X+1 0 0 1 1 X 1 1 0 0 X 0 X+1 1 X X 0 X X+1 X+1 X 0 1 1 X+1 0 1 X+1 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 1 0 1 1 0 0 0 1 1 1 1 X+1 X+1 X X+1 1 1 X+1 X+1 X+1 X X+1 X X X 0 X+1 0 X+1 1 X+1 1 1 0 1 X+1 1 X X+1 1 X+1 0 0 X X X 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 1 1 1 0 1 1 0 0 1 X+1 1 1 1 X X+1 X+1 0 X+1 0 1 X 1 X+1 1 0 0 X+1 X X 0 0 X+1 X 0 X+1 0 1 0 X+1 1 1 1 X+1 X 1 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 0 0 X X X 0 X 0 X X 0 0 X X X X 0 X X X X 0 0 0 0 0 X X X X 0 X 0 0 X 0 X 0 X 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 X 0 0 X X X 0 X 0 0 X X 0 X 0 0 X X X 0 X X X 0 X X X 0 0 X X 0 X 0 X 0 X X X 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 0 0 0 0 0 0 X X 0 0 X X X X X 0 0 0 X X X X X X X 0 X 0 X X 0 X 0 0 0 0 0 0 0 0 X X X 0 0 X 0 0 X X 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 generates a code of length 78 over Z2[X]/(X^2) who´s minimum homogenous weight is 40. Homogenous weight enumerator: w(x)=1x^0+23x^40+26x^41+68x^42+70x^43+132x^44+172x^45+213x^46+262x^47+348x^48+372x^49+483x^50+558x^51+533x^52+614x^53+544x^54+582x^55+526x^56+506x^57+451x^58+402x^59+316x^60+288x^61+217x^62+148x^63+137x^64+98x^65+143x^66+178x^67+197x^68+264x^69+370x^70+556x^71+603x^72+714x^73+949x^74+1168x^75+1220x^76+1098x^77+1370x^78+1458x^79+1290x^80+966x^81+946x^82+880x^83+640x^84+408x^85+346x^86+368x^87+195x^88+132x^89+103x^90+106x^91+145x^92+136x^93+262x^94+242x^95+331x^96+388x^97+416x^98+564x^99+519x^100+632x^101+556x^102+592x^103+549x^104+550x^105+463x^106+386x^107+321x^108+250x^109+224x^110+142x^111+138x^112+56x^113+54x^114+40x^115+25x^116+10x^117+10x^118+2x^119+2x^120+4x^122+1x^128 The gray image is a linear code over GF(2) with n=156, k=15 and d=40. This code was found by Heurico 1.16 in 98.7 seconds.