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 1 1 1 1 1 1 1 1 1 1 1 1 X 1 X X X X 1 1 1 1 1 X X X X X 1 X X 1 0 X^2 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 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 0 0 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 0 0 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 0 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 0 0 X^2 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 0 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 0 0 0 X^2 0 0 X^2 0 X^2 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 0 0 0 0 X^2 generates a code of length 76 over Z2[X]/(X^3) who´s minimum homogenous weight is 60. Homogenous weight enumerator: w(x)=1x^0+156x^60+434x^64+4x^66+640x^68+252x^70+1046x^72+744x^74+9777x^76+824x^78+1116x^80+212x^82+611x^84+12x^86+342x^88+171x^92+36x^96+5x^100+1x^128 The gray image is a linear code over GF(2) with n=304, k=14 and d=120. This code was found by Heurico 1.16 in 33.3 seconds.