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 0 X 1 X X^2 1 1 0 X 1 X 1 1 1 X^2 1 0 X 1 1 X 1 X X^2 X 1 1 X X 1 1 0 X 0 X 0 0 X X^2+X 0 X^2 X^2+X X 0 X X X^2 X^2 X^2+X 0 X X^2+X 0 X X^2 X X X X^2+X X^2+X X X 0 X 0 X^2+X 0 X^2+X X^2 X^2 X^2 X 0 X^2 X^2+X X X X^2 X^2 0 X 0 X^2 X^2 0 X X^2 0 0 0 X X 0 X^2+X X 0 X^2 X 0 X 0 X^2+X X^2 X X X^2 0 X^2+X X^2+X X X^2 0 X^2 X 0 0 X^2+X X^2+X X^2+X X X^2 X X^2 X^2 0 X^2 X X^2+X X^2+X X X X X^2+X 0 X 0 X^2+X X^2+X X 0 X^2 X^2+X 0 X^2 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 0 X^2 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 0 0 0 0 0 X^2 0 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 0 0 X^2 0 0 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 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 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 0 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 0 0 X^2 generates a code of length 57 over Z2[X]/(X^3) who´s minimum homogenous weight is 48. Homogenous weight enumerator: w(x)=1x^0+57x^48+44x^49+119x^50+156x^51+206x^52+246x^53+287x^54+366x^55+377x^56+464x^57+398x^58+364x^59+249x^60+212x^61+158x^62+112x^63+98x^64+52x^65+48x^66+24x^67+32x^68+6x^69+11x^70+2x^71+3x^72+2x^74+1x^76+1x^82 The gray image is a linear code over GF(2) with n=228, k=12 and d=96. This code was found by Heurico 1.16 in 1.12 seconds.