The generator matrix 1 0 0 0 1 1 1 0 1 1 1 X X 0 1 1 0 X 1 1 0 1 X X 0 1 1 1 X 1 0 1 1 1 1 X X 0 0 1 1 1 1 1 1 1 1 X 1 X 1 X X 0 1 X X X X 1 X 1 1 0 1 X 1 1 1 0 1 0 X 1 1 0 0 1 0 1 0 0 0 1 1 1 X 0 X+1 1 1 X 1 X 1 1 1 0 0 1 1 0 X X X+1 X 0 1 0 X X+1 1 0 1 1 1 1 X+1 X X+1 X+1 1 X 0 X+1 1 X+1 1 X X X X 1 1 1 1 X 0 X X+1 X 1 X+1 1 0 X+1 1 X X+1 1 X X+1 X X 0 X 0 0 1 0 1 1 0 1 0 X+1 X X 1 1 1 1 X X+1 0 0 X 0 0 1 1 0 X+1 X+1 1 X 1 0 X 1 X+1 X 1 1 X+1 1 X 0 1 1 1 1 X+1 X X X X+1 1 0 1 0 X X X+1 0 X+1 1 1 X 0 0 X X X+1 1 1 0 X+1 0 1 X 1 1 1 0 0 0 1 1 0 1 1 1 0 X 1 0 1 X+1 1 X+1 X+1 1 X 1 X X 1 X X+1 0 X X+1 0 0 0 1 0 X+1 0 0 1 X 1 1 1 1 X+1 X X+1 0 1 0 X+1 X 1 1 X+1 0 1 X+1 1 1 X X+1 X+1 1 X+1 X+1 0 0 0 X X+1 1 0 1 X 1 0 0 X+1 0 0 0 0 X 0 0 0 0 X 0 X X X 0 0 0 0 0 0 X X X 0 X 0 X X X 0 X X 0 X 0 0 0 0 X 0 X 0 0 X X X X X 0 X 0 X 0 X X X 0 0 X 0 0 X 0 0 0 X 0 0 0 X X 0 0 0 X 0 X 0 0 0 0 0 0 X 0 0 0 0 0 X 0 X 0 0 X X X X 0 X 0 0 0 X 0 X 0 0 X 0 0 X 0 X X X X X 0 0 X X X 0 0 0 X X X 0 0 X X 0 0 0 0 X X 0 0 X 0 X 0 0 X 0 X X X 0 X 0 X X 0 0 0 0 0 0 X 0 0 0 X 0 X 0 0 X X 0 X 0 X 0 0 X X X 0 X X 0 X 0 0 0 0 0 X 0 0 X 0 X 0 X X X X 0 X 0 0 0 0 X X X X 0 X X 0 X X 0 0 X X X 0 0 X 0 X X 0 0 0 X 0 0 0 0 0 0 0 X 0 0 0 0 0 X X X X 0 X X X 0 X X X 0 X 0 X X 0 0 X 0 0 X 0 X X 0 X X X 0 X 0 X 0 0 X 0 X X X X 0 X 0 0 X X X 0 0 0 X 0 0 X 0 0 X 0 X 0 0 X X generates a code of length 78 over Z2[X]/(X^2) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+189x^68+320x^70+497x^72+468x^74+505x^76+424x^78+448x^80+298x^82+303x^84+282x^86+179x^88+106x^90+41x^92+22x^94+11x^96+2x^100 The gray image is a linear code over GF(2) with n=156, k=12 and d=68. This code was found by Heurico 1.16 in 7.61 seconds.