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 X 0 1 X 0 1 1 X 1 1 0 1 1 1 1 X 1 1 1 1 0 X 1 1 1 1 0 1 1 0 X X 0 1 0 0 1 0 X 0 X^2+X 0 X^2+X 0 X^2+X 0 X^2+X X^2 X^2+X 0 X^2+X X 0 X^2 0 0 X^2 X^2+X X^2+X X^2+X X^2+X X X X^2+X X X^2+X X X^2+X X^2+X 0 X X^2 X^2 0 X^2 X^2+X X^2+X X X^2 X X X^2+X X^2 X X^2+X 0 X X^2 X X X^2+X X^2+X X X X X 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 0 X^2 0 X^2 0 0 X^2 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 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 0 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 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 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 X^2 0 0 X^2 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 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 0 0 X^2 X^2 0 0 0 0 0 0 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 0 0 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 0 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 generates a code of length 60 over Z2[X]/(X^3) who´s minimum homogenous weight is 50. Homogenous weight enumerator: w(x)=1x^0+37x^50+4x^51+127x^52+20x^53+228x^54+128x^55+267x^56+352x^57+263x^58+520x^59+272x^60+520x^61+254x^62+352x^63+229x^64+128x^65+192x^66+20x^67+95x^68+4x^69+32x^70+20x^72+11x^74+10x^76+6x^78+2x^80+1x^82+1x^88 The gray image is a linear code over GF(2) with n=240, k=12 and d=100. This code was found by Heurico 1.16 in 1.37 seconds.