The generator matrix 1 0 1 1 1 X^2+X 1 1 X^2 1 1 X 1 1 0 1 1 1 X^2 1 0 1 X 1 1 X^2+X 1 1 1 1 1 1 0 1 1 0 1 X^2+X 1 1 1 1 1 X^2+X 1 X^2 1 1 X^2 1 1 1 1 1 0 1 0 1 1 X^2+X X^2+X+1 1 0 X+1 1 X X^2+1 1 X^2+X+1 X^2 1 0 X+1 1 1 X^2+X 1 X 1 X^2+1 X^2+1 1 X^2 X+1 X X^2+1 X^2 X^2+X 1 X 1 1 X+1 1 X^2+X+1 0 X^2+1 X X^2+1 1 X^2+1 X X X X X+1 1 X^2 X+1 X^2+1 X 0 0 0 X 0 X^2+X 0 X^2+X 0 X^2+X X X^2 X X^2+X X^2+X 0 X^2 0 X^2+X X 0 X^2+X X^2+X X^2+X X^2 X^2+X 0 X X^2+X X^2+X X^2 0 X^2 0 X^2 X^2+X X^2 X^2 0 0 X^2+X 0 X^2+X 0 X^2+X X^2+X X X 0 X X X^2 X X X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 0 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 X^2 0 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 0 0 0 0 0 X^2 0 X^2 0 0 X^2 0 X^2 0 0 0 0 X^2 0 X^2 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 0 0 0 0 generates a code of length 56 over Z2[X]/(X^3) who�s minimum homogenous weight is 48. Homogenous weight enumerator: w(x)=1x^0+193x^48+36x^49+382x^50+232x^51+733x^52+544x^53+832x^54+728x^55+996x^56+728x^57+788x^58+536x^59+583x^60+224x^61+360x^62+40x^63+133x^64+4x^65+62x^66+43x^68+8x^70+4x^72+1x^76+1x^80 The gray image is a linear code over GF(2) with n=224, k=13 and d=96. This code was found by Heurico 1.16 in 3.41 seconds.