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 X^2 X^2 X X X^2 X 1 1 0 0 1 0 0 X^2 X X 1 1 X X X^2 1 X 1 0 X 0 0 0 X X^2+X X 0 X^2 X^2 X X^2+X X X 0 0 0 X^2 X^2+X X^2+X X^2 X^2 X X^2+X 0 X^2+X X^2 X^2+X 0 X^2 0 X^2+X X X X X X X^2+X 0 X^2 0 X^2 X^2+X 0 0 0 0 X X^2 X^2+X X^2+X X^2 X 0 0 0 0 0 X 0 X X X^2+X 0 0 0 X X X 0 X^2 X^2+X X 0 X^2 X^2 0 0 X^2+X X^2 X^2+X X^2+X X X^2 X^2 X^2+X X^2+X X^2 X^2+X X X 0 0 X^2 0 X^2 X^2 X 0 X^2 X X X^2 X^2+X X^2 X^2+X X^2 0 X^2+X X^2 X^2+X 0 X^2+X 0 0 0 X X 0 X^2+X X X^2 X X^2 0 X X^2 X^2+X X X^2 X^2 X X^2+X X^2 X X^2 X 0 X^2+X X^2+X X^2 0 0 X^2+X X^2 X^2+X 0 0 X^2+X X^2+X X^2+X 0 X^2 X^2+X X^2 X X X 0 X 0 0 0 0 X^2+X X 0 X^2+X X^2+X 0 0 0 0 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 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 0 0 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 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 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 X^2 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 0 X^2 0 0 0 0 X^2 X^2 0 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+229x^48+4x^49+408x^50+76x^51+601x^52+236x^53+816x^54+444x^55+1045x^56+548x^57+1028x^58+420x^59+887x^60+228x^61+514x^62+84x^63+345x^64+8x^65+154x^66+77x^68+22x^70+11x^72+2x^74+3x^76+1x^80 The gray image is a linear code over GF(2) with n=228, k=13 and d=96. This code was found by Heurico 1.16 in 4.73 seconds.