The generator matrix 1 0 0 0 0 1 1 1 1 0 1 1 X 1 0 X 1 X 0 X 1 1 1 1 0 1 1 0 0 X 1 1 0 0 1 1 0 1 1 1 X 1 0 1 X 1 0 1 1 1 X 1 0 1 1 1 1 0 1 X X X 1 X X 0 X 0 1 0 1 0 0 0 0 X 1 0 0 1 0 0 0 0 0 0 0 X 0 0 X X X 1 X+1 1 1 1 1 1 1 X+1 1 X+1 X+1 1 0 1 X 1 1 1 X+1 X 0 0 X 1 X 1 X 1 X X X X 1 X+1 1 X+1 1 1 1 1 X X 1 1 1 1 0 0 1 0 1 1 0 1 1 1 0 X 1 0 1 0 0 0 1 0 0 0 1 0 X 0 1 X+1 1 X+1 1 0 X 1 1 X 1 X+1 1 X+1 X 0 0 1 1 X+1 X+1 X X 0 1 X 1 0 X+1 0 1 1 X X X 0 1 X+1 X+1 1 1 X 0 0 X X X+1 X X+1 X X X+1 X+1 1 0 X 0 X+1 X 1 0 1 1 0 0 0 0 0 0 0 0 1 0 1 1 X 1 1 X X X X+1 X+1 X+1 X+1 0 1 X X+1 X 0 1 X+1 0 X X+1 X X X+1 X+1 X+1 1 1 X 1 X+1 X 0 0 1 1 0 1 X 0 X+1 0 X 0 X X 0 X+1 X X 1 0 0 1 0 X+1 X 0 1 X X 0 0 X+1 X+1 0 0 1 X X+1 X 0 0 0 0 1 1 0 1 0 1 X X+1 1 1 X X+1 X+1 X+1 X+1 1 0 X 1 X+1 0 1 0 X 0 X 0 0 X 1 X 0 1 1 1 X+1 X+1 X+1 X 0 X 0 X X+1 X 1 1 1 X+1 0 1 1 1 1 X+1 X X 0 0 X+1 X+1 X X X X X+1 X 1 0 1 X 1 1 1 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 X X X X X X X X X X 0 X 0 X 0 0 X X 0 0 X X 0 0 X 0 X 0 0 X X X X X X X 0 0 X X X 0 0 0 X X X X X 0 0 0 0 0 0 0 0 0 X 0 0 0 X X X X X 0 0 X X 0 X X X X 0 0 0 X X X X 0 0 0 X 0 X X 0 X 0 0 X X X X 0 0 0 0 0 X X X X X 0 0 0 0 X X 0 0 0 X 0 0 X 0 X 0 0 X 0 0 0 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+154x^68+390x^70+460x^72+484x^74+492x^76+432x^78+408x^80+322x^82+342x^84+240x^86+184x^88+102x^90+60x^92+10x^94+11x^96+4x^98 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 3.99 seconds.