The generator matrix 1 0 0 0 0 0 0 1 1 1 X 0 1 1 0 1 1 0 1 X X 0 0 0 0 1 1 1 1 X 1 1 1 1 1 X 1 0 1 1 1 X X 0 1 1 X 1 1 0 X X X X 1 1 0 0 X 1 1 1 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X 1 1 1 1 1 X+1 X+1 1 1 1 X+1 1 1 1 X+1 1 1 X 0 0 X 1 X X X+1 0 1 1 0 1 1 1 X 1 X X+1 0 1 1 1 X 0 1 X 0 X+1 X 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 X+1 1 1 X X+1 1 X 0 X 1 X+1 X+1 0 X+1 X 0 X+1 0 1 1 1 X+1 0 X+1 0 X 1 X+1 1 X+1 X 1 0 X X X+1 X+1 0 1 X+1 1 1 X X X+1 X 1 0 0 0 0 0 1 0 0 0 0 0 0 0 X 0 0 0 X 0 0 0 0 X 0 X 0 X X X X 0 0 0 X 0 X 0 1 X+1 1 1 1 1 X+1 1 1 X+1 1 1 1 X+1 1 1 X 1 X+1 1 X+1 X+1 0 X+1 1 X 1 X 1 1 X X 0 0 0 0 1 0 0 0 1 1 1 1 0 X X X 1 X+1 X+1 X+1 0 1 0 1 0 1 0 X X+1 1 X+1 X+1 X X 0 0 0 0 1 1 1 0 0 0 1 X 0 0 1 X X X X X+1 1 1 X 1 1 X 0 0 1 X 0 0 1 0 0 0 0 0 1 0 1 0 X+1 1 1 1 0 X+1 0 1 X+1 0 0 1 0 X X 1 1 1 0 X X+1 X 1 X X+1 X+1 0 1 0 X X+1 X X 1 1 1 X X+1 X X+1 X+1 X X+1 X 0 0 X 1 0 0 1 X+1 X X+1 X 1 1 1 0 0 0 0 0 0 1 1 X+1 X 1 0 X 1 1 0 1 X X X+1 0 1 X+1 0 1 X+1 0 0 X+1 X+1 X X 1 X X+1 X 0 1 1 0 0 0 1 0 X X X+1 0 X+1 1 1 1 1 0 0 X+1 X+1 X X+1 X+1 0 0 X+1 1 X+1 1 X 0 0 0 0 0 0 0 X X 0 0 X 0 0 X X 0 0 0 X X 0 X X 0 0 X 0 X X X 0 0 0 0 X 0 X X X X 0 X 0 X 0 X 0 X 0 X X 0 0 X X 0 0 0 0 0 0 0 X 0 0 0 generates a code of length 67 over Z2[X]/(X^2) who´s minimum homogenous weight is 53. Homogenous weight enumerator: w(x)=1x^0+106x^53+186x^54+330x^55+512x^56+638x^57+742x^58+954x^59+1214x^60+1296x^61+1462x^62+1648x^63+1911x^64+2066x^65+2153x^66+2190x^67+2124x^68+2118x^69+1993x^70+1782x^71+1559x^72+1366x^73+1169x^74+962x^75+674x^76+472x^77+418x^78+272x^79+175x^80+122x^81+63x^82+54x^83+20x^84+8x^85+4x^86+1x^88+1x^90+1x^96+1x^102 The gray image is a linear code over GF(2) with n=134, k=15 and d=53. This code was found by Heurico 1.11 in 57.6 seconds.