The generator matrix 1 0 0 0 0 0 0 0 1 1 1 X 1 1 0 1 0 X 1 X 0 X 1 1 1 0 0 1 X X 1 0 0 1 1 X X 1 X X X 0 1 X 0 X 1 1 1 0 1 0 X 0 1 1 1 1 0 X 1 1 X X 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X X 1 1 1 1 1 1 1 1 1 X+1 1 1 1 X 1 1 1 X+1 1 1 X 1 1 X+1 X 0 1 0 X 1 1 X 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 X 1 1 1 1 X+1 1 1 X 1 X+1 X 0 0 1 1 1 X+1 1 0 1 X+1 1 X X+1 X+1 X+1 0 X 1 1 X+1 0 X 1 0 X+1 X 0 1 X X X X 0 X 0 1 1 0 X 0 X 1 0 0 0 0 1 0 0 0 0 0 1 X 1 0 1 X 0 1 1 1 X+1 1 0 X+1 X 1 X 1 X+1 X X X 0 0 X+1 X+1 X+1 1 X X X 1 1 X 0 1 1 1 X 1 X X+1 X 1 1 X X+1 X 1 0 X+1 X 1 X X 1 X+1 0 0 0 0 0 0 1 0 0 0 1 0 1 1 X X+1 1 X X+1 0 X X X+1 X 1 X 0 1 X 1 X X+1 0 0 1 0 1 X X+1 0 X+1 0 1 1 1 0 X+1 0 X+1 1 X+1 X+1 0 X 0 X+1 0 1 X+1 0 X X 1 0 0 X+1 1 0 0 0 0 0 0 0 0 1 0 0 1 X 0 X+1 1 1 1 0 X 1 1 1 X+1 1 0 X+1 X+1 X 1 X 1 X 0 1 1 X X+1 0 0 X 0 X 0 X+1 X X X 0 X+1 1 1 0 1 X X+1 X X X X X 1 X X+1 X 1 X 1 X+1 1 0 0 0 0 0 0 0 1 0 1 X+1 X+1 1 X+1 0 X 0 0 1 1 X X+1 X+1 X 0 1 X+1 0 X+1 X+1 X 1 0 X+1 1 1 1 1 X+1 0 X 0 0 X X+1 X+1 0 X+1 0 0 X+1 1 1 1 X X+1 0 1 X+1 1 0 X 0 X+1 1 X+1 1 0 0 0 0 0 0 0 0 0 1 X X 1 1 1 1 1 X+1 X+1 X+1 0 0 0 X X 0 1 1 1 X+1 X+1 X 0 X+1 X+1 X+1 1 1 X X+1 X+1 1 X+1 0 X X 1 1 0 X+1 X X+1 0 X X+1 X 1 0 1 X+1 X+1 1 0 X X 1 1 0 1 0 generates a code of length 68 over Z2[X]/(X^2) who´s minimum homogenous weight is 52. Homogenous weight enumerator: w(x)=1x^0+75x^52+100x^53+359x^54+450x^55+724x^56+932x^57+1287x^58+1444x^59+1845x^60+2040x^61+2651x^62+3014x^63+3232x^64+3956x^65+3976x^66+4302x^67+4133x^68+4366x^69+4063x^70+4068x^71+3735x^72+3264x^73+2720x^74+2232x^75+1779x^76+1372x^77+1093x^78+702x^79+587x^80+300x^81+313x^82+150x^83+116x^84+42x^85+34x^86+22x^87+25x^88+12x^89+15x^90+4x^92+1x^98 The gray image is a linear code over GF(2) with n=136, k=16 and d=52. This code was found by Heurico 1.11 in 256 seconds.