The generator matrix 1 0 1 1 1 X^2+X 1 1 0 1 1 X^2+X 1 X^2+X 1 1 1 0 1 1 0 1 1 X^2+X 0 1 X^2+X 1 1 1 1 0 1 1 1 X^2+X X^2+X 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 1 1 0 1 X+1 X^2+X 1 1 0 X+1 1 X^2+X X^2+1 1 X^2+X 1 X+1 0 X^2+1 1 X+1 0 1 X^2+X X^2+1 1 1 X^2+X 1 0 X+1 X^2+1 X+1 1 0 X+1 X^2+X 1 1 X^2+1 X X^2+1 0 X^2+X 1 1 X+1 X^2+X X^2 X X^2+1 1 X+1 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 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 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 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 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 0 0 X^2 0 0 X^2 X^2 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 generates a code of length 54 over Z2[X]/(X^3) who´s minimum homogenous weight is 42. Homogenous weight enumerator: w(x)=1x^0+25x^42+14x^43+87x^44+88x^45+145x^46+386x^47+251x^48+972x^49+431x^50+1868x^51+696x^52+2816x^53+865x^54+2820x^55+705x^56+1864x^57+433x^58+966x^59+212x^60+392x^61+99x^62+90x^63+60x^64+12x^65+37x^66+28x^68+11x^70+7x^72+2x^74+1x^76 The gray image is a linear code over GF(2) with n=216, k=14 and d=84. This code was found by Heurico 1.16 in 11.5 seconds.