The generator matrix 1 0 1 1 1 X^2 1 1 X X 1 1 X^2 1 1 X^2+X 1 1 0 1 1 X 1 1 X^2+X X^2+X X X X X^2 X^2 X^2 X X^2 X X^2+X X^2 0 X^2 0 X^2+X 0 X 1 1 1 1 X 1 1 1 1 X 1 0 1 0 1 1 0 X+1 1 X^2+X+1 0 1 1 X^2 1 1 X X+1 1 X^2+X X+1 1 X 1 1 X X^2+1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X^2 X X+1 X^2+1 1 X^2+1 X^2+X+1 X^2+X X^2+1 X^2 X^2+1 X X^2+X 0 0 X 0 0 0 0 X X^2+X X^2+X X X X^2 X^2+X X^2+X X^2+X X^2+X X^2+X X^2 X^2 X^2 X^2+X X^2 X^2 X 0 X^2 0 0 X X^2+X X^2+X X^2 X X^2 X^2+X X^2+X X X^2 0 X^2 X 0 X^2 0 X X^2+X X 0 X X^2 X^2 X^2+X X X 0 0 0 0 X X^2 X^2+X X^2+X X X^2 X^2+X X^2 X^2+X X^2+X 0 X X X^2+X X^2 X^2 X^2+X X 0 X^2 0 X 0 0 X X^2+X 0 X^2 X X^2 X^2+X X^2+X X^2 X^2+X X^2 X^2 X^2+X X X X^2 X^2+X X^2+X X^2+X X^2+X 0 0 0 0 X^2+X 0 X X^2 X^2 generates a code of length 56 over Z2[X]/(X^3) who´s minimum homogenous weight is 52. Homogenous weight enumerator: w(x)=1x^0+232x^52+178x^54+229x^56+220x^58+95x^60+50x^62+9x^64+8x^68+1x^80+1x^84 The gray image is a linear code over GF(2) with n=224, k=10 and d=104. This code was found by Heurico 1.16 in 71.4 seconds.