The generator matrix 1 0 0 0 0 0 0 1 1 1 X 1 1 0 1 1 0 X 0 1 1 0 X 1 0 1 1 0 0 1 1 0 X 0 0 X 1 1 X 1 0 X 1 1 0 X X X 0 1 0 0 X X 1 X 0 1 1 0 1 1 X 0 0 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X 0 X X 0 0 0 X X 0 X 0 1 1 1 1 1 X+1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 X+1 X 1 X+1 X+1 1 1 1 1 1 0 X+1 X+1 0 X 0 0 1 0 0 0 0 0 0 0 0 0 0 0 X X X X 0 0 X 1 1 1 1 1 X+1 1 1 1 X+1 1 0 1 1 1 X+1 0 X X X 0 X+1 X+1 1 X+1 0 1 1 X 1 X X 1 0 1 0 1 X+1 X X 1 0 X+1 1 0 X 1 X 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 1 X+1 1 1 X X X+1 0 X X+1 1 0 X+1 1 1 X X+1 0 X X 0 1 0 X+1 1 1 X X+1 X+1 X 1 1 0 0 0 X X+1 X+1 X+1 1 X X 0 1 X+1 0 0 1 X+1 0 0 0 0 0 1 0 0 0 1 1 1 0 X X 1 X+1 X+1 1 1 0 1 X X 1 0 X+1 X+1 X+1 1 X+1 1 1 1 X+1 X+1 X X X 1 X 0 X X+1 X X+1 1 X+1 1 X 1 0 0 1 1 0 1 X X 1 1 0 1 0 X 1 X+1 X X+1 1 0 0 0 0 0 1 0 1 0 X+1 1 1 0 X+1 0 X+1 1 X 1 X X+1 X+1 0 X+1 1 X+1 X 0 0 X X X X+1 1 1 0 0 X 0 X+1 X+1 X X+1 0 X+1 X 1 0 1 X+1 X+1 X X 1 X+1 X X X 1 1 0 X 0 1 X+1 1 0 X 1 0 0 0 0 0 0 1 1 X+1 X 1 X 1 1 0 X+1 0 1 0 0 0 X X+1 X+1 1 0 0 X+1 0 1 X+1 X+1 X+1 1 X X 1 X 0 0 1 1 1 X+1 X+1 1 X+1 1 0 1 1 X X X+1 X 0 0 X 0 0 1 0 X 0 X+1 X 1 1 0 0 0 0 0 0 0 0 X X 0 0 0 0 X 0 0 0 X X X X X X X X 0 X X X X 0 0 X X 0 X 0 X X 0 X 0 X X 0 0 0 X X 0 0 X 0 0 X 0 0 X 0 0 0 0 X 0 X 0 X 0 X generates a code of length 69 over Z2[X]/(X^2) who�s minimum homogenous weight is 55. Homogenous weight enumerator: w(x)=1x^0+108x^55+215x^56+338x^57+494x^58+732x^59+835x^60+878x^61+1153x^62+1384x^63+1504x^64+1710x^65+1853x^66+1946x^67+2035x^68+1986x^69+2194x^70+2072x^71+1957x^72+1880x^73+1600x^74+1432x^75+1175x^76+934x^77+704x^78+520x^79+361x^80+306x^81+171x^82+114x^83+87x^84+26x^85+17x^86+12x^87+18x^88+6x^89+2x^90+4x^92+3x^94+1x^102 The gray image is a linear code over GF(2) with n=138, k=15 and d=55. This code was found by Heurico 1.11 in 61.4 seconds.