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 X^2 X X 0 X^2 0 1 X X X 0 1 1 X X 0 X^2 1 0 1 0 1 1 1 0 1 X^2 X X^2 1 X 0 1 X^2 1 0 X 0 0 0 X X^2+X X 0 X^2 X^2 X X^2+X 0 X^2+X X X^2 X^2+X X^2+X 0 0 X X^2+X X^2+X 0 0 X^2+X X X^2 0 0 X X X X^2 X^2+X X X 0 X^2 X X X^2+X X^2 0 X^2+X X^2 X^2+X X^2 X X X^2 X^2 X X^2 X^2+X X^2+X X X X X X X 0 X^2 X^2 X X^2+X 0 0 X 0 X X X^2+X 0 0 0 X X^2 X X^2+X X^2 X^2+X X^2 X^2 X^2 0 X X X^2 X^2+X X^2 X X X^2 X X^2+X 0 X X 0 0 0 X^2 X^2 0 X^2+X 0 X^2+X 0 X 0 0 X X X 0 X^2 X X X^2 0 0 X^2+X 0 X X X^2+X X^2+X X X X X^2 X^2+X X 0 0 0 X X 0 X^2+X X 0 X 0 X X^2+X X^2+X X^2 X^2 0 X^2 X X^2+X 0 0 X^2+X X^2+X X 0 X 0 X X 0 0 X^2 X^2+X X X^2 0 X^2+X X X^2+X X^2+X 0 X^2 X^2 X^2+X X^2+X X^2 0 X^2 X^2 0 X X X^2+X X^2+X X^2+X X^2+X X^2+X X^2+X 0 0 X X^2 X^2 X X^2 X^2 X 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 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 X^2 X^2 0 0 X^2 0 0 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 0 0 0 0 X^2 0 0 X^2 0 0 X^2 0 0 0 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 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 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 0 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 0 X^2 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+72x^56+98x^57+196x^58+248x^59+380x^60+466x^61+582x^62+706x^63+902x^64+1206x^65+1187x^66+1424x^67+1485x^68+1312x^69+1340x^70+1192x^71+918x^72+778x^73+569x^74+428x^75+246x^76+206x^77+171x^78+86x^79+81x^80+30x^81+37x^82+12x^83+9x^84+10x^86+1x^88+3x^90+1x^94+1x^104 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 21.6 seconds.