The generator matrix 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 0 X X 1 X 1 1 0 1 X X X X 0 0 1 0 0 X 0 X 1 0 0 1 1 X 0 0 1 1 1 1 1 1 1 1 0 1 0 0 0 0 0 0 1 X 1 1 X+1 0 0 X 1 0 1 1 1 1 0 X 1 X X+1 1 X+1 1 1 0 X 0 1 X 1 X 1 1 1 X 1 0 1 X 1 1 X 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 X+1 X+1 X 0 1 X+1 1 X 1 X+1 X X X+1 1 1 1 0 1 X+1 0 X+1 0 X X X X+1 X+1 0 1 1 X+1 X+1 1 X 1 X+1 0 0 X X 0 X 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 X 1 X+1 0 1 X X+1 0 X+1 X 0 0 1 X 0 1 1 X+1 0 0 X 1 1 1 1 X+1 X X+1 0 1 1 1 X X+1 1 1 X+1 X+1 1 X 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 X 1 X+1 X X+1 X+1 1 0 X+1 X 1 X+1 0 X+1 0 0 0 1 X 0 X+1 1 1 0 X+1 X 0 X+1 X X+1 X+1 X+1 0 X X+1 1 1 0 X 1 1 X 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 X X+1 0 1 0 X+1 X+1 0 0 X 0 X+1 1 0 X+1 X X+1 X+1 1 0 X 0 X+1 1 X 0 1 1 X+1 1 0 0 X X+1 X 1 0 0 1 X+1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 X+1 0 X X+1 0 1 1 0 1 X 0 X 0 X+1 X+1 X+1 1 0 1 0 1 X X+1 0 X+1 1 X X+1 X+1 1 X+1 X+1 X+1 X+1 X X X+1 X X+1 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X 0 0 0 X 0 X X 0 0 X X 0 0 0 X X X X X X 0 X 0 X X X 0 X X 0 X 0 X 0 0 0 0 0 0 0 X 0 0 0 0 0 0 generates a code of length 57 over Z2[X]/(X^2) who´s minimum homogenous weight is 38. Homogenous weight enumerator: w(x)=1x^0+38x^38+64x^39+136x^40+158x^41+179x^42+266x^43+367x^44+496x^45+617x^46+712x^47+914x^48+994x^49+1111x^50+1258x^51+1462x^52+1576x^53+1594x^54+1680x^55+1719x^56+1870x^57+1770x^58+1850x^59+1724x^60+1578x^61+1403x^62+1222x^63+1187x^64+930x^65+817x^66+778x^67+578x^68+456x^69+415x^70+288x^71+191x^72+112x^73+106x^74+72x^75+37x^76+22x^77+12x^78+2x^79+4x^80+1x^86+1x^90 The gray image is a linear code over GF(2) with n=114, k=15 and d=38. This code was found by Heurico 1.16 in 98.5 seconds.