The generator matrix 1 0 0 0 0 1 1 1 X^2 1 0 1 1 X 1 1 1 0 X^2+X 1 X^2+X X^2+X 1 X X^2 1 1 X^2+X 1 1 X^2+X 1 1 1 1 X^2+X X^2 X^2+X X^2 1 0 0 0 1 1 1 X 1 1 X^2+X 1 0 0 0 1 1 1 1 X X^2 0 X 1 1 X^2+X 1 1 0 1 0 0 0 0 X+1 X^2 X^2 X^2+X+1 1 X X^2+1 1 1 X^2+X+1 X X X^2 X^2 X 1 0 1 1 X^2+X+1 1 1 X+1 X^2 1 1 1 X+1 X^2+X 1 1 0 X X^2+X 1 0 1 X^2+X+1 X^2+X+1 X^2+1 1 X^2+X X^2 1 X+1 1 0 1 X+1 X^2+X X^2+1 0 X^2 X 0 X^2+X X+1 X^2+X+1 1 0 0 0 0 1 0 0 0 1 X^2+1 1 X^2 X+1 X^2+X+1 X^2+1 X^2 X X^2+X 0 1 1 1 0 X X^2+X+1 X X^2+X+1 X^2+1 0 X^2+1 1 0 1 1 1 X X X^2 X^2+1 1 1 1 X^2+X 1 X 0 1 0 X^2+X X+1 X+1 1 1 X^2 X^2+X X^2+X+1 X^2+1 X^2+X X^2 X^2 X^2 0 1 1 X^2+X+1 X^2 X X+1 0 0 0 0 1 0 1 X^2 1 1 X^2+1 X+1 0 0 X^2 0 1 X X X^2+X+1 X 1 X^2+X+1 X^2+X+1 1 X^2 X+1 X X^2+1 X+1 1 X^2 X^2+X 0 X^2+1 0 X^2+X X^2+1 0 X^2+X+1 X^2 X 1 X+1 X^2+1 X^2+1 0 X^2+1 X^2 X^2+1 X+1 X^2+X X^2+X+1 1 X^2 X^2+X 1 X^2+1 X^2+X X^2 1 X X^2+X X^2+1 X^2+X+1 1 X^2 0 0 0 0 0 1 1 X^2+1 0 1 1 X^2 X^2+1 X^2+X X^2+1 X+1 X^2+X X+1 X^2+1 X^2+X X X^2+1 X^2+1 X^2+1 0 X^2+1 X^2+X+1 0 X^2+1 X X^2 X^2+X X^2+1 0 X^2+X+1 X+1 0 X+1 X^2+X+1 1 1 X^2+1 X X X 0 X^2+1 X^2 X X^2+X+1 X^2 X^2+X X 0 X^2+X+1 X+1 1 X^2+X 1 1 X^2+X+1 1 X^2 1 X+1 X^2+1 X X^2+X+1 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2+X X^2+X X^2+X X X X^2+X X^2+X X X^2+X X^2+X X X^2+X X^2+X X X X X^2+X X^2+X X^2+X X X^2 X^2+X X^2+X X^2+X X^2+X X^2 X^2 X^2+X X^2+X X X^2 generates a code of length 67 over Z2[X]/(X^3) who´s minimum homogenous weight is 56. Homogenous weight enumerator: w(x)=1x^0+222x^56+702x^57+1532x^58+2002x^59+3369x^60+4162x^61+6747x^62+7452x^63+9634x^64+10398x^65+13203x^66+11838x^67+13015x^68+10440x^69+10491x^70+7906x^71+6529x^72+4136x^73+3313x^74+1652x^75+1120x^76+532x^77+340x^78+178x^79+90x^80+28x^81+20x^82+12x^83+4x^84+2x^85+2x^86 The gray image is a linear code over GF(2) with n=268, k=17 and d=112. This code was found by Heurico 1.13 in 210 seconds.