The generator matrix 1 0 0 0 0 1 1 1 1 1 1 1 X X X 0 0 0 X X X 0 1 1 0 1 1 1 1 1 0 1 1 X 1 1 1 1 X 0 X X 0 X X 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 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 X 0 1 X X X 1 X 0 X 0 X+1 0 X 0 0 X+1 X 0 X+1 0 1 1 0 1 0 0 X 1 0 0 X X 0 0 0 X 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 1 0 0 1 0 1 1 0 1 0 1 0 0 1 X 1 1 1 1 1 0 0 X 1 X+1 0 1 X+1 1 0 1 1 0 0 0 1 1 1 1 0 1 1 0 0 1 0 0 X 0 0 X 0 X 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 1 0 1 1 1 0 0 0 1 1 0 0 X+1 X+1 X 1 1 X+1 1 0 1 1 1 1 1 0 X+1 X+1 X 0 0 0 0 X 0 1 0 1 0 0 0 1 1 1 1 0 0 0 1 X 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 X+1 0 X+1 0 X+1 X X X+1 X 0 X+1 X X+1 1 1 X+1 0 X+1 X 1 0 1 1 0 X+1 1 1 0 0 1 0 X 1 1 0 X 0 0 X 0 X 0 X 0 X 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 X 0 0 0 0 0 X 0 X X 0 X 0 X 0 X X 0 0 0 X X X X 0 0 X X X 0 X X X 0 0 0 X X 0 0 0 0 0 0 0 0 0 0 X 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 X 0 0 0 0 X X X 0 0 X X 0 X X 0 0 X 0 X X X X X X X X 0 0 X 0 X X X 0 0 X 0 X X 0 0 X 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 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 X X 0 X X X 0 0 0 0 0 0 X X X 0 0 X X 0 0 0 0 X X 0 0 0 X 0 X 0 0 X 0 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 0 0 0 0 X 0 X 0 0 X X X 0 0 X X 0 X X 0 X 0 0 X X X 0 X 0 0 X 0 0 0 X X 0 X X 0 0 0 X 0 X 0 0 X X 0 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 0 0 0 0 0 X 0 X X 0 X X X 0 0 X 0 X X X X X 0 X 0 X X X X 0 X 0 X 0 0 0 X X X 0 0 X X X 0 X X 0 0 0 0 X 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 generates a code of length 89 over Z2[X]/(X^2) who´s minimum homogenous weight is 40. Homogenous weight enumerator: w(x)=1x^0+13x^40+12x^41+7x^42+6x^43+24x^44+26x^45+35x^46+42x^47+60x^48+64x^49+107x^50+114x^51+130x^52+174x^53+193x^54+258x^55+233x^56+220x^57+301x^58+326x^59+357x^60+410x^61+353x^62+404x^63+408x^64+410x^65+420x^66+326x^67+355x^68+360x^69+263x^70+306x^71+241x^72+242x^73+216x^74+182x^75+199x^76+174x^77+218x^78+258x^79+279x^80+392x^81+523x^82+688x^83+793x^84+972x^85+1114x^86+1172x^87+1361x^88+1308x^89+1294x^90+1218x^91+1118x^92+906x^93+852x^94+664x^95+510x^96+404x^97+281x^98+254x^99+201x^100+226x^101+183x^102+200x^103+201x^104+212x^105+251x^106+262x^107+329x^108+376x^109+362x^110+384x^111+392x^112+404x^113+373x^114+366x^115+374x^116+368x^117+390x^118+366x^119+281x^120+248x^121+226x^122+258x^123+187x^124+200x^125+138x^126+80x^127+87x^128+62x^129+64x^130+48x^131+37x^132+16x^133+25x^134+10x^135+12x^136+6x^137+1x^138+8x^140+2x^142+1x^144 The gray image is a linear code over GF(2) with n=178, k=15 and d=40. This code was found by Heurico 1.16 in 99.2 seconds.