The generator matrix 1 0 1 1 1 X^3+X^2+X 1 X 1 X^3 1 1 X^2 1 1 1 X^2+X 1 1 X^3+X^2 1 X^3+X 1 1 1 1 1 1 0 X^2+X 1 1 1 1 1 1 X^3 X^3+X^2+X 1 1 X^3 1 1 X^3+X^2 1 X^3+X^2+X 1 X X 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 X+1 X^2+X X^3+X^2+1 1 X^3+X^2 1 X^2+X+1 1 X^3+X 1 1 X^3 X+1 X^3+X^2+X 1 X^3+X^2+X+1 X^2 1 X 1 X+1 X^3+X^2+X+1 X^2+1 X^3+1 X^2+1 0 1 1 X^3+X^2+X X^3+X^2+X+1 X^3+X^2+1 X^3 X^2+X X^3+X^2+1 1 1 X^2+X+1 0 1 X^3+1 X^2 1 X^2+X 1 X^3+X 1 X^3+X X^3+X^2+1 X^3+X+1 1 1 X^2+X+1 X^2+1 X^2+X+1 X^3 X^3+X+1 X^2+X+1 X+1 X^3+1 X+1 0 0 X^2 0 X^3+X^2 X^2 0 X^2 X^3+X^2 X^3+X^2 0 X^2 X^3+X^2 X^2 X^3 X^3+X^2 0 X^3 X^2 0 X^3+X^2 0 X^3 X^3 0 X^3 X^3 0 0 0 X^3+X^2 X^3+X^2 X^2 X^2 X^3 0 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^2 0 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^3 0 X^3 X^2 X^2 X^2 0 0 X^3 X^3 0 0 0 0 X^3 0 0 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 0 0 0 X^3 X^3 X^3 X^3 X^3 0 0 X^3 X^3 X^3 0 0 0 X^3 X^3 0 0 0 0 X^3 0 X^3 X^3 0 X^3 0 X^3 X^3 0 X^3 0 X^3 X^3 0 0 X^3 0 0 X^3 X^3 0 0 X^3 0 0 0 0 0 X^3 0 X^3 X^3 0 0 X^3 X^3 X^3 X^3 0 0 X^3 0 0 X^3 X^3 0 X^3 X^3 0 X^3 0 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 X^3 0 X^3 X^3 0 0 0 0 0 X^3 0 X^3 X^3 X^3 0 X^3 X^3 X^3 X^3 0 0 X^3 0 X^3 0 X^3 generates a code of length 62 over Z2[X]/(X^4) who´s minimum homogenous weight is 57. Homogenous weight enumerator: w(x)=1x^0+82x^57+296x^58+432x^59+388x^60+562x^61+682x^62+512x^63+417x^64+352x^65+228x^66+72x^67+24x^68+20x^69+10x^70+6x^73+8x^75+2x^77+2x^88 The gray image is a linear code over GF(2) with n=496, k=12 and d=228. This code was found by Heurico 1.16 in 0.406 seconds.