The generator matrix 1 0 0 0 0 0 1 1 1 0 1 1 X 1 0 1 1 X 1 1 X 0 0 1 X 1 1 1 1 X 1 1 0 X X 1 X 1 0 1 0 1 1 0 1 X 1 X 0 X 1 1 1 0 0 1 1 1 X X 1 0 X 1 1 1 1 1 X 1 1 1 1 1 0 1 1 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 X 1 1 1 1 X+1 1 1 1 1 X 0 X X+1 X+1 1 1 0 X X 1 X+1 1 0 1 0 1 1 X+1 1 X 1 1 1 0 1 X+1 0 X+1 X 1 0 X+1 1 1 X 1 1 1 1 X 0 X X X 0 X X 1 X+1 1 X+1 0 1 1 1 X+1 0 0 1 0 0 0 0 0 0 0 1 1 1 X+1 1 X 1 X+1 0 0 X+1 X+1 X X+1 1 X 1 1 X 0 1 X+1 1 1 1 X X 1 X+1 X X 0 1 1 1 0 X+1 1 X 0 X+1 1 X X 0 1 1 X X+1 1 0 X+1 X X 1 1 X+1 1 X X 0 0 X X+1 0 X+1 1 X X+1 1 0 0 0 0 1 0 0 0 1 1 1 X 1 X+1 X+1 X+1 X 0 0 X X+1 X+1 0 1 X+1 X X 0 0 X+1 X+1 X+1 0 X 1 0 0 X 0 1 X+1 X+1 0 X+1 X+1 0 X+1 X+1 0 X 1 X 1 X 1 0 X+1 0 X+1 X 0 X+1 X 0 X+1 X+1 X X X+1 1 X 1 X 1 0 0 0 1 1 X 0 1 0 0 0 0 1 0 1 1 0 X+1 X 0 X X+1 1 0 X+1 X+1 X+1 1 X X X 1 X+1 0 X+1 0 X 1 0 1 X+1 X+1 1 X+1 1 0 1 1 X X 1 1 X+1 X 0 X 0 1 X X X 1 X+1 X+1 1 X 1 X 1 X 0 0 X X 1 X X X+1 X 1 X+1 X X 0 X 0 X X+1 X+1 0 0 0 0 0 1 1 0 X+1 X+1 1 X X+1 X+1 X 1 X+1 0 0 X+1 X 1 X+1 0 1 X X X X X 1 X X+1 X 0 0 1 1 X+1 0 1 1 X X+1 0 X+1 X+1 X+1 1 X 1 0 X+1 X 0 0 0 1 1 X+1 X X 1 X 1 0 X+1 0 X X X 1 1 X X+1 1 1 X 1 X 1 0 0 0 0 0 0 X 0 X X X 0 X X 0 X X 0 0 X 0 X X 0 X 0 0 X X X 0 X 0 X X X X 0 X 0 X 0 X 0 0 0 0 0 X X X X X X 0 X X X 0 X X 0 0 X 0 0 0 X 0 X 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X 0 X 0 X X 0 0 0 0 0 X 0 0 X X X X X X 0 0 X X 0 0 X X 0 X X 0 0 0 0 X X 0 X 0 X 0 0 X X X 0 X X X X 0 0 0 X X X X 0 0 0 X X 0 0 0 0 0 X 0 X 0 0 0 generates a code of length 81 over Z2[X]/(X^2) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+240x^68+646x^70+1042x^72+1286x^74+1481x^76+1620x^78+1883x^80+1848x^82+1810x^84+1546x^86+1207x^88+794x^90+512x^92+284x^94+137x^96+40x^98+4x^100+1x^104+1x^112+1x^124 The gray image is a linear code over GF(2) with n=162, k=14 and d=68. This code was found by Heurico 1.16 in 96.5 seconds.