The generator matrix 1 0 1 1 1 X^3+X^2+X 1 1 0 1 X^3+X^2+X 1 1 1 1 X^3 1 X^3+X 1 1 0 1 X^3+X 1 1 1 1 1 1 1 1 X^2 1 1 1 1 X 1 1 X^3+X 1 1 X^3+X X^2+X X^2 0 1 1 1 1 0 1 1 X X^2+X 1 1 0 1 X+1 X^3+X^2+X X^2+1 1 X^3+X^2+1 0 1 X^3+X^2+X 1 X+1 X^3+1 X^2+X+1 X^3 1 X^3+X 1 X^3+X^2+X+1 0 1 X^3+X 1 1 X^3+X^2+X+1 X^3+X^2+1 X+1 X^3+X^2+1 X^3+X^2+X+1 X^3+1 X^2 1 X+1 X^3+X+1 X^3+X+1 X 1 X^3+X^2+1 X^2+X 1 X^3 X^3+1 1 1 1 1 X^3+X^2 X^3+X+1 X^3+X^2+1 X^2+1 1 X+1 X^3 1 1 X^2+1 0 0 0 X^2 0 0 0 0 X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3 X^2 X^3+X^2 X^2 X^3 X^3 X^2 X^3 X^3 X^2 X^3+X^2 X^3 X^3+X^2 X^2 0 X^2 0 X^2 0 X^3+X^2 X^3 X^3 X^3 0 X^2 X^3+X^2 0 0 X^2 0 X^3 X^2 X^3 X^2 X^3 X^3 X^3 0 X^2 X^3+X^2 X^2 0 0 X^2 0 0 0 0 X^3+X^2 X^3 X^3+X^2 X^2 X^2 X^3+X^2 X^3 0 X^3+X^2 0 X^3 0 X^3 X^3 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^2 X^2 0 X^3 X^2 X^2 X^3 X^3+X^2 X^3 0 X^2 X^3+X^2 X^2 X^3 0 0 0 X^3 X^3 X^2 X^3+X^2 X^2 X^2 0 X^3 X^2 0 X^3+X^2 0 0 X^3+X^2 X^3 X^3 0 generates a code of length 57 over Z2[X]/(X^4) who´s minimum homogenous weight is 52. Homogenous weight enumerator: w(x)=1x^0+90x^52+270x^53+302x^54+608x^55+515x^56+572x^57+506x^58+588x^59+279x^60+252x^61+83x^62+4x^63+8x^64+8x^65+2x^66+2x^68+2x^69+2x^70+1x^78+1x^84 The gray image is a linear code over GF(2) with n=456, k=12 and d=208. This code was found by Heurico 1.16 in 0.281 seconds.