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 X X 0 0 X X^2 X 1 X 1 1 1 1 1 X X X X^2 X^2 X X^2 0 1 1 X X X 0 X 0 0 0 X X^2+X X 0 X^2 X^2 X X^2+X 0 X^2+X X X^2 X^2+X 0 X^2+X 0 X X^2+X X^2+X 0 0 X^2+X X X^2 0 X 0 X^2 X 0 X^2 X^2+X 0 0 X^2 0 X^2 X^2 X^2 X^2+X X^2+X X^2+X X X X X X 0 X^2 0 X^2+X X 0 0 X 0 X X X^2+X 0 0 0 X X^2 X X^2+X X^2 X^2+X X^2 X^2 0 X^2 X X X^2 X^2+X X^2 X X X^2 X X^2+X X X X X X X X^2 X^2 X^2+X X^2+X 0 X X^2+X X^2+X X^2+X X^2 0 0 X X^2 X^2+X 0 X^2+X 0 X^2 X^2+X X 0 0 0 X X 0 X^2+X X 0 X 0 X X^2+X X^2+X X^2 X^2 0 X^2 X^2+X X 0 0 X^2+X X^2+X X 0 X 0 X X 0 X^2+X X^2 X^2+X X X 0 0 0 0 X^2 X X^2 0 X X^2 X X X^2 X^2 X^2 X^2+X X^2+X 0 X X^2+X 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 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 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 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 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 0 X^2 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 0 0 X^2 0 0 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 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 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 0 X^2 X^2 0 0 X^2 X^2 generates a code of length 57 over Z2[X]/(X^3) who´s minimum homogenous weight is 46. Homogenous weight enumerator: w(x)=1x^0+125x^46+409x^48+64x^49+730x^50+220x^51+1098x^52+480x^53+1643x^54+736x^55+2151x^56+1056x^57+2128x^58+824x^59+1668x^60+416x^61+1170x^62+256x^63+674x^64+32x^65+286x^66+12x^67+126x^68+52x^70+13x^72+8x^74+4x^76+1x^78+1x^86 The gray image is a linear code over GF(2) with n=228, k=14 and d=92. This code was found by Heurico 1.16 in 17.6 seconds.