The generator matrix 1 0 0 0 1 1 1 0 1 1 1 1 X X X 1 X X 1 0 1 1 0 0 1 1 1 1 1 0 0 1 1 0 1 1 1 0 1 1 1 1 0 X 1 0 0 X 1 1 X X 1 X 0 X 1 1 1 1 0 0 X X 0 1 0 0 0 1 1 1 X 0 X+1 X+1 1 1 X 1 1 1 1 1 1 X X 0 0 0 X+1 1 0 1 1 1 1 X 0 0 0 1 0 1 X X+1 1 1 1 X 0 1 1 X 0 0 1 1 X 1 1 X+1 X 0 1 X 0 0 0 0 1 0 1 1 0 1 0 X+1 X+1 X X X+1 1 X X X+1 1 1 0 X 0 1 X+1 1 X+1 0 X 0 0 X 1 1 1 0 1 X+1 X+1 X+1 0 X X 1 0 1 1 X+1 X X 1 1 X+1 X+1 1 1 X X+1 X 1 0 1 1 1 0 0 0 1 1 0 1 1 1 0 1 X X+1 0 X+1 1 1 X+1 0 X X 0 1 X+1 0 X+1 X+1 1 0 0 X+1 X 1 X X X+1 X X+1 0 X X X X X+1 0 X 0 0 X X+1 X+1 X 1 X+1 1 X X+1 X+1 1 1 0 1 X+1 X+1 0 0 0 0 X 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 X X X 0 X X X 0 X X X X X 0 X X 0 X X 0 X X 0 0 0 X 0 0 X 0 0 0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 0 X 0 X X X X 0 0 X 0 X X X X 0 0 0 X X 0 X X 0 0 X X X 0 X 0 X X 0 0 X X 0 0 X X X X X 0 X 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 X X X 0 X X 0 0 X X X 0 X X 0 X 0 0 0 X X 0 X 0 0 X X 0 0 0 0 X 0 X 0 X X 0 X 0 X X X 0 X 0 X X X 0 X 0 0 0 0 0 0 0 X X X 0 X X X X X 0 0 X 0 X 0 X 0 0 X X X X X X X 0 X 0 0 X X 0 0 0 X 0 0 0 0 0 0 X X X 0 X 0 0 0 0 0 X 0 0 0 X 0 generates a code of length 64 over Z2[X]/(X^2) who´s minimum homogenous weight is 54. Homogenous weight enumerator: w(x)=1x^0+81x^54+102x^55+143x^56+206x^57+223x^58+256x^59+250x^60+248x^61+244x^62+240x^63+264x^64+238x^65+226x^66+234x^67+191x^68+234x^69+168x^70+136x^71+111x^72+92x^73+61x^74+46x^75+54x^76+6x^77+18x^78+10x^79+9x^80+2x^82+1x^84+1x^86 The gray image is a linear code over GF(2) with n=128, k=12 and d=54. This code was found by Heurico 1.16 in 2.32 seconds.