The generator matrix 1 0 1 1 1 0 1 1 0 1 1 X 1 1 0 1 1 0 1 1 1 0 1 0 1 0 1 1 1 0 1 1 X 1 0 1 X 1 1 1 1 X 0 1 X 1 0 1 X 1 1 1 0 0 0 1 1 1 X X 1 1 1 0 1 1 1 1 1 0 1 1 0 1 1 0 1 1 0 X+1 1 X X+1 1 0 X+1 1 X+1 0 X+1 1 X 1 X+1 1 X+1 0 X 1 1 0 1 0 1 0 1 X+1 X+1 0 X 1 1 X+1 1 1 1 X+1 1 0 X 0 0 1 1 1 X+1 X 1 0 1 1 X+1 1 1 0 X+1 0 0 0 0 X 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X X X X X X X X 0 0 X X X 0 0 0 X 0 X 0 X X X 0 X X 0 X X 0 0 X X X 0 0 0 0 0 X 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 X X X X X X 0 0 X X X X X 0 0 X X 0 X X X X X 0 X 0 X X 0 X 0 0 X X X 0 0 X 0 0 0 X 0 0 X 0 0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 0 X X X 0 X X X X X 0 X 0 0 X 0 X X 0 0 0 0 0 X X X X X 0 X 0 X 0 0 X X X X 0 0 X 0 X X 0 0 X X X X 0 0 0 X 0 0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 0 X X 0 0 X 0 X X X 0 0 0 X 0 X 0 X 0 X X 0 0 0 X X 0 X 0 0 X X X X 0 0 0 0 X X 0 0 X X X X 0 X X X 0 X 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 X 0 X X X 0 X X 0 0 X X 0 X 0 0 X X X X X 0 X 0 0 0 0 0 X 0 0 0 0 X 0 X 0 X 0 X 0 X X X X X 0 X X 0 0 X X X 0 0 0 0 0 0 0 0 0 X 0 0 X 0 0 0 X X X X X 0 0 X 0 X X X 0 0 X X X X X 0 0 X 0 0 X X X X X 0 0 X 0 X X 0 0 0 X X 0 X 0 X 0 0 X 0 0 X X 0 X 0 0 0 0 0 0 0 0 0 0 X 0 0 X 0 X X 0 0 X 0 X X X X X X X 0 X X X X 0 X X 0 0 0 X X X X X X X X X X 0 0 X 0 0 X 0 X X 0 X 0 0 X X X X 0 X 0 X 0 0 0 0 0 0 0 0 0 0 X 0 0 X X X 0 X 0 0 0 X X 0 X X X X 0 0 0 X 0 0 X X X 0 0 0 0 X 0 0 X 0 X X 0 0 X X X X 0 0 0 X 0 X X 0 X X X X 0 0 0 0 generates a code of length 69 over Z2[X]/(X^2) who´s minimum homogenous weight is 56. Homogenous weight enumerator: w(x)=1x^0+27x^56+10x^57+75x^58+52x^59+157x^60+110x^61+155x^62+184x^63+197x^64+260x^65+224x^66+268x^67+238x^68+268x^69+226x^70+288x^71+184x^72+258x^73+174x^74+188x^75+142x^76+102x^77+94x^78+40x^79+50x^80+16x^81+48x^82+4x^83+22x^84+18x^86+5x^88+7x^90+1x^92+3x^94 The gray image is a linear code over GF(2) with n=138, k=12 and d=56. This code was found by Heurico 1.16 in 3.34 seconds.