The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X 0 X 0 0 X^2 X X X 1 1 1 X 1 1 X X X X X 1 X^2 1 0 X^2 1 1 X X^2 1 1 1 0 X 0 X 0 0 X X^2+X 0 0 X X^2+X X^2 0 X^2+X X^2 X^2+X X^2 X X X^2+X X^2 X X 0 0 X^2 0 X X X^2+X X 0 X 0 X^2+X X X X^2 0 X^2 X 0 X X^2+X X^2 0 X^2+X X X X X X^2 X 0 X X^2+X X X^2 X X 0 X X X X^2 X X 0 0 X X 0 X^2+X X 0 0 X^2+X X 0 X X^2 X X^2 0 X^2+X X X^2+X 0 X^2+X 0 X 0 X^2 X X X^2 X X^2+X X^2 X^2 X X^2+X X^2 X^2+X 0 X X X X X^2+X X^2+X 0 X^2 0 X X X^2 X^2 X X X^2 X^2+X X^2 X^2+X X^2+X X^2 0 X^2+X X^2+X 0 X^2 0 X^2+X X X 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 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 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 0 0 X^2 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 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^2 0 0 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 0 0 0 X^2 0 0 0 0 0 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 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 0 0 generates a code of length 68 over Z2[X]/(X^3) who´s minimum homogenous weight is 56. Homogenous weight enumerator: w(x)=1x^0+201x^56+220x^58+32x^59+780x^60+136x^61+702x^62+352x^63+1518x^64+640x^65+1640x^66+864x^67+2184x^68+912x^69+1636x^70+672x^71+1587x^72+320x^73+724x^74+128x^75+656x^76+40x^77+174x^78+185x^80+24x^82+40x^84+12x^88+4x^92 The gray image is a linear code over GF(2) with n=272, k=14 and d=112. This code was found by Heurico 1.16 in 22.6 seconds.