The generator matrix 1 0 0 0 0 0 0 1 1 1 X 0 1 1 0 1 1 X 1 0 1 1 X X 1 0 1 1 X 1 1 1 1 1 X 0 1 1 0 1 0 0 1 0 1 0 X 1 1 1 1 1 1 X 1 1 1 1 1 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X 0 0 X X X X X 0 0 X X 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X+1 1 X+1 X+1 1 0 1 1 0 X X X+1 X+1 1 X 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 X+1 1 X X+1 1 1 X 0 X+1 X+1 X 0 1 0 1 X X+1 X+1 X X+1 0 1 X 1 1 1 0 0 1 X+1 0 X+1 X+1 X X+1 1 X 0 1 0 X 1 0 X 0 1 0 0 0 0 1 0 0 0 0 0 0 0 X 0 0 0 X X X X X 1 X+1 X+1 X+1 1 1 X+1 1 1 1 1 X+1 1 1 1 0 X+1 X+1 X+1 0 X 1 X 0 X X 1 X 1 X 0 X X X 0 1 X+1 0 0 X X+1 X 0 0 X+1 0 0 0 0 1 0 0 0 1 1 1 1 0 X X X X+1 1 1 1 1 X+1 0 X 1 1 0 X 0 0 X+1 X+1 X+1 0 X+1 1 1 1 X X+1 0 X 1 X+1 X+1 X+1 0 0 1 1 1 0 1 1 X X 0 X+1 0 X X+1 X+1 X X 0 0 0 0 0 0 1 0 1 0 X+1 1 1 1 0 X+1 0 0 0 1 1 0 X X X+1 1 X+1 0 1 1 X 1 0 X 0 X+1 1 X+1 X+1 X+1 X 1 X 1 0 X 0 0 X+1 X 1 0 X X+1 X X 0 0 X+1 X 0 X 1 0 X+1 X+1 0 0 0 0 0 0 1 1 X+1 X 1 0 X 1 1 0 0 X+1 X+1 0 0 X+1 1 0 1 X X X+1 1 1 0 X 1 1 X+1 0 0 1 1 1 X+1 0 X X 0 0 0 X X 1 X X X+1 X 0 1 X+1 0 1 X+1 0 X 1 X+1 0 0 0 0 0 0 0 0 X X 0 0 X 0 0 X X 0 X 0 0 0 0 0 X X X 0 0 X X X X X 0 X X 0 X 0 0 X 0 0 0 0 X X X X X X X 0 X 0 X 0 0 0 X 0 0 X 0 0 generates a code of length 65 over Z2[X]/(X^2) who´s minimum homogenous weight is 51. Homogenous weight enumerator: w(x)=1x^0+62x^51+195x^52+294x^53+455x^54+596x^55+817x^56+988x^57+1143x^58+1372x^59+1529x^60+1706x^61+1813x^62+1936x^63+2104x^64+2288x^65+2288x^66+2136x^67+1960x^68+1834x^69+1630x^70+1360x^71+1154x^72+948x^73+672x^74+488x^75+351x^76+214x^77+171x^78+108x^79+75x^80+48x^81+15x^82+6x^83+5x^84+3x^86+1x^88+1x^90+1x^98 The gray image is a linear code over GF(2) with n=130, k=15 and d=51. This code was found by Heurico 1.11 in 53.2 seconds.