The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 X 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 1 1 X X 1 X X 1 1 1 X 1 1 1 1 1 X 1 X 1 1 0 X 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 X X X X X X X X X X X X X X X 0 X X X X X 0 0 X X X X 0 X 0 X X X 0 X 0 0 X 0 0 0 0 X 0 0 0 0 0 0 0 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 0 X 0 X X 0 X 0 0 0 X 0 X 0 X 0 X X 0 X X X 0 X X 0 X 0 X X 0 X 0 X X 0 X 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 X X X X X X X 0 X 0 X X X 0 X 0 0 X 0 X X 0 0 X X X 0 X 0 X X 0 0 0 X 0 X 0 X 0 0 0 X X X 0 X X X X 0 X 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 X X X X X X X 0 0 X 0 0 0 0 X X 0 X X X 0 X X 0 X X X 0 0 0 0 X 0 0 0 0 X X 0 X X 0 X 0 0 X X 0 X 0 X X X X X 0 0 0 X X 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X 0 0 0 0 X X X X X X 0 X X X 0 0 X 0 X X X X X X 0 X 0 0 X X 0 0 0 X 0 X 0 0 0 X 0 X 0 X 0 X 0 X 0 0 X X X 0 0 0 X X X 0 0 X 0 0 0 X 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 X 0 0 X X X X X X 0 X X X 0 0 0 0 0 X X 0 X 0 X X X X X X 0 X 0 X 0 X 0 0 0 0 X 0 0 X X X X 0 0 0 X 0 0 X X 0 X 0 0 X 0 X 0 X X 0 X X 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 0 X X 0 X X 0 X 0 X 0 X X 0 X 0 X 0 X 0 X 0 X 0 X X 0 0 0 0 0 X 0 0 0 X X X 0 X X X X X X X 0 0 X 0 X X 0 0 X 0 X 0 X 0 X X X X 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 0 0 X X X X 0 X X 0 0 X 0 X 0 0 0 0 X X 0 0 0 X X X X 0 0 X X X X 0 0 X X X X 0 0 0 0 X X X X X 0 0 X 0 0 0 X X X X X X X 0 X X X X X 0 0 0 0 0 0 0 0 0 X 0 0 0 X 0 0 0 0 0 X X 0 X 0 0 0 X X X 0 0 X X X X X X X 0 0 0 X X X 0 X X X 0 0 0 0 X 0 0 X X X 0 0 X 0 0 0 0 0 X 0 X 0 0 X X 0 0 X X X X X X 0 X X 0 0 0 0 0 0 0 0 0 0 X 0 0 X 0 0 0 0 X 0 0 X 0 X 0 0 X X X X X 0 0 0 X 0 X X X 0 0 0 0 0 X 0 X 0 X X X 0 0 0 X 0 X X X 0 X 0 0 0 0 0 X X X 0 0 X 0 0 0 0 X X X 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X 0 X X X X X X 0 0 0 X 0 0 X X X X 0 X 0 0 X X X 0 0 0 0 0 X X 0 X X 0 X 0 0 X 0 X X X X 0 0 0 X X 0 X X 0 X 0 X X 0 0 0 X X 0 0 0 X 0 0 0 0 X X 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X 0 0 X X X X X 0 X 0 X 0 0 X X X 0 X 0 X 0 X 0 0 0 X 0 0 0 X 0 0 X 0 0 0 X X 0 0 X X 0 X X X 0 0 X X 0 X 0 0 X X X X X X X 0 X 0 X X generates a code of length 84 over Z2[X]/(X^2) who´s minimum homogenous weight is 64. Homogenous weight enumerator: w(x)=1x^0+121x^64+419x^68+757x^72+16x^74+1039x^76+336x^78+2182x^80+1696x^82+3198x^84+1696x^86+2249x^88+336x^90+1091x^92+16x^94+721x^96+362x^100+110x^104+34x^108+3x^112+1x^148 The gray image is a linear code over GF(2) with n=168, k=14 and d=64. This code was found by Heurico 1.16 in 85.5 seconds.