The generator matrix 1 0 0 0 1 1 1 1 X^3+X^2 1 1 X^3 X^3 1 X X^3+X X^2+X 1 1 0 1 X^2+X 1 1 1 X^3+X X^3+X^2 1 1 0 X^3+X 1 1 X 1 X^2 X^3+X 1 1 X^3+X^2+X 1 1 1 1 1 1 1 1 1 1 0 X^3+X^2+X 1 1 0 1 1 X^3 1 X^2+X X^3+X^2+X 0 X 0 1 0 0 X X^2+1 X^3+1 X^2 1 X^3+X+1 X^3+X^2+X 1 1 X^3+X^2+X+1 0 X^2+X 1 1 X+1 0 X^2 1 X^2+X+1 X^3+X X 1 1 X^3 X^3+X^2+1 X 1 X^3+X^2+1 X+1 1 X^2 X^3+X^2+X X X^3+X^2+X+1 X^3+X^2 1 X^2+X+1 X^3+1 X^2+X+1 X^3+1 X^3+1 X^2+X X^3+X^2+X X^3+X+1 X^3 X^2+X+1 1 1 X^2 X^3+X^2 X^2+X X^3+X^2+X+1 X^2+X 1 X^3+X^2 X^3+X 1 X^3+X 1 0 0 1 0 0 X^2 1 X^2+1 1 X^2+1 X^3+1 X^3+X^2+X+1 X^2+X X^3+X 1 X^3+X X^3+X 0 X^3+X+1 1 X^3+X X^3+X^2 X^3+X^2 X^2+X+1 X^2+1 X^2+1 X^3+X^2+1 X^3+X^2 X+1 1 X^2+X+1 X^2+X X^3+X^2+X+1 X^2+X X^3+X^2 X^3+X 1 X^3+X^2+1 X^2+X X^2+X+1 0 X^3+X+1 X^3+X^2+X+1 X^3 X X^2+X 1 X X+1 X+1 X^3+X^2+X X^3+X^2+X+1 X^2 X^3+X 0 X^2+X X^3+X+1 X^3+X^2+X+1 X^2+1 1 X^3+X+1 1 X^2+X 0 0 0 1 1 X^2+X+1 X^2 X^3+X^2+X+1 X^2+X+1 X^2+1 X^3+X X^3+X^2+X X+1 X^3+X^2+X X^3+X+1 1 X^3+X+1 X^3+X^2+1 X^3+X^2+X+1 X^3+X^2+X X^2+X+1 X^2+X X^3 X^3+X^2 X^2+1 X^2+1 0 X^3+X^2+X X^3+X 1 0 X^3+1 1 0 X^2+1 1 X+1 X^2 X^3 X^3+X X^3+X X+1 X^3 X^3+X+1 X^3+X^2 X^2+1 X^2 0 X^3+X+1 X^2+X+1 X^2 X^3+1 0 X^3+X^2+1 1 X+1 X^3+X+1 0 X^2+X X^3+X X^3+X^2+X+1 X^3+1 X^3+X^2+X+1 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2 0 X^2 X^3+X^2 0 X^3+X^2 X^3 X^3 X^3 X^3 X^3+X^2 X^2 X^3 X^2 0 0 0 X^3 X^3 X^2 X^3 X^2 X^3 X^3+X^2 0 X^3+X^2 X^3 X^2 X^2 X^3+X^2 X^3+X^2 X^3 X^3+X^2 0 0 X^2 X^3+X^2 0 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^3 X^3 X^3 X^3 X^3+X^2 X^3+X^2 X^3 generates a code of length 63 over Z2[X]/(X^4) who´s minimum homogenous weight is 55. Homogenous weight enumerator: w(x)=1x^0+510x^55+1712x^56+4182x^57+8390x^58+13640x^59+20790x^60+27876x^61+34864x^62+36604x^63+35945x^64+29254x^65+21692x^66+12950x^67+7424x^68+3646x^69+1564x^70+766x^71+194x^72+88x^73+16x^74+8x^75+14x^76+6x^77+4x^81+2x^82+2x^83 The gray image is a linear code over GF(2) with n=504, k=18 and d=220. This code was found by Heurico 1.16 in 737 seconds.