The generator matrix 1 0 0 0 1 1 1 1 0 1 1 1 X X X 1 1 1 X 0 1 1 1 1 0 1 X 0 X 1 0 X X 1 1 0 X X X 1 1 1 1 X X 1 1 1 1 1 X X 0 1 1 1 1 0 1 0 0 1 0 0 1 1 0 1 1 1 1 0 X 0 X+1 0 1 0 X+1 1 0 0 1 0 1 1 X+1 1 1 1 1 X 1 1 X X 0 1 1 1 0 1 0 X+1 X+1 1 X 1 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 1 1 0 0 1 1 X X+1 1 1 0 1 0 1 0 0 0 1 X 1 0 1 X+1 X+1 X 0 X X+1 X 1 X 1 1 X+1 1 X X+1 1 1 0 X X+1 0 X 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 1 0 1 X+1 1 1 X+1 0 X 0 0 X 1 X+1 0 1 1 1 X+1 X X 1 0 X 0 1 0 X X+1 X+1 X+1 X+1 1 X+1 X+1 X 0 X+1 X+1 1 1 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 X X 0 X X X 0 X X X X X 0 0 0 0 0 X 0 X 0 0 X X X 0 X 0 X X X X 0 0 X 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 X X X X X X X X X 0 0 X X X 0 X 0 X X 0 X X X X 0 0 X 0 X X 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 X 0 0 X 0 0 0 X X X 0 X 0 0 X X 0 X X X X 0 X X 0 X 0 0 0 0 0 X X 0 X 0 X 0 X X 0 X 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 X X X 0 0 X X 0 X X X 0 0 0 0 X 0 X 0 0 X 0 0 0 X X 0 0 X 0 X 0 0 X X X 0 X 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 X X 0 X 0 X X X 0 X X X 0 0 X 0 X 0 0 0 X X X 0 0 X X 0 0 0 0 X X 0 X X X X 0 X 0 X 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 X X X X X 0 X 0 X 0 X 0 X X 0 0 X 0 X X 0 X X 0 0 0 0 X X 0 X X X 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 X X 0 0 0 X X X X 0 0 X X 0 0 X X 0 X X 0 0 0 0 X 0 X 0 X X 0 X X 0 0 X X X 0 0 0 0 0 0 generates a code of length 57 over Z2[X]/(X^2) who´s minimum homogenous weight is 40. Homogenous weight enumerator: w(x)=1x^0+45x^40+34x^41+105x^42+132x^43+239x^44+266x^45+461x^46+540x^47+702x^48+858x^49+1079x^50+1242x^51+1484x^52+1764x^53+1863x^54+2134x^55+2224x^56+2332x^57+2212x^58+2224x^59+1838x^60+1798x^61+1549x^62+1308x^63+1080x^64+842x^65+616x^66+490x^67+492x^68+264x^69+245x^70+110x^71+70x^72+30x^73+51x^74+8x^75+11x^76+4x^77+10x^78+4x^79+5x^80+1x^82+1x^88 The gray image is a linear code over GF(2) with n=114, k=15 and d=40. This code was found by Heurico 1.16 in 97.3 seconds.