The generator matrix 1 0 1 1 1 X^2+X 1 1 0 1 X^2+X 1 1 1 0 1 1 X^2+X X^2+X 1 1 0 1 X 1 1 1 1 1 1 1 0 1 0 1 1 X^2 1 1 1 1 X^2+X 1 1 1 1 X 1 1 X^2 X 1 1 X^2 1 X^2 X 1 0 X 0 1 1 X^2 0 1 1 1 0 1 X+1 X^2+X 1 1 0 X+1 1 X^2+X 1 X^2+1 0 X+1 1 X^2+X X^2+1 1 1 0 X+1 1 X^2+X 1 X^2+1 0 X^2+1 X+1 X^2+1 X^2+X+1 X 1 0 1 X+1 X^2+1 1 X^2+X X^2 X^2+X X+1 1 1 X X^2+1 X^2+X+1 1 X^2+X X^2+X+1 1 1 1 1 X X^2+X+1 1 1 X^2+1 1 X^2 1 X X 1 1 X^2+X+1 X+1 X^2+X+1 0 0 X^2 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 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 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 X^2 X^2 0 X^2 0 0 0 X^2 0 0 0 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 0 X^2 0 0 0 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 0 0 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 0 0 0 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 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 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 0 0 0 0 0 generates a code of length 68 over Z2[X]/(X^3) who´s minimum homogenous weight is 62. Homogenous weight enumerator: w(x)=1x^0+164x^62+381x^64+352x^66+290x^68+366x^70+321x^72+128x^74+22x^76+10x^78+7x^80+2x^86+1x^88+2x^94+1x^96 The gray image is a linear code over GF(2) with n=272, k=11 and d=124. This code was found by Heurico 1.16 in 94.7 seconds.