The generator matrix 1 0 1 1 1 X^2+X 1 1 X^2 1 X 1 1 1 X^2+X 0 1 X^2+X 1 1 1 1 X^2 1 1 1 X^2 1 1 0 1 1 X^2+X 1 X 1 0 1 1 X X 1 0 1 X 1 1 X^2+X 1 0 1 1 1 X^2+X 0 1 1 1 1 X^2+X 1 1 X^2+X 1 1 X 1 1 0 1 1 0 X^2+X+1 1 X X+1 1 1 1 0 X^2+X+1 X^2+X 1 1 X 1 X+1 X^2+1 X^2+X 0 1 X^2+1 1 X+1 1 X+1 X^2+X 1 0 X^2 1 X^2+X 1 1 1 1 0 1 1 1 1 X+1 1 1 0 1 X^2+X 1 X^2+X X^2+X+1 X^2+X 1 0 X^2+1 X^2+X X^2+X+1 X+1 1 1 X^2+1 1 X^2+X+1 X^2+1 X^2 X^2+X+1 X+1 0 0 X 0 X^2+X 0 0 0 X^2 X^2 X^2 X 0 X X^2+X X^2+X X X X^2+X X 0 X X 0 X X^2+X X^2 X X X^2 X 0 X^2 X^2 X^2+X 0 X^2 0 X X^2+X X^2 X^2+X X X^2+X X^2+X X^2 X^2+X X^2+X X^2+X X^2+X X^2+X X X 0 X X^2 0 X^2 X^2+X X 0 0 X^2 X^2+X 0 X^2 X X^2 0 0 0 X 0 0 X X^2 X^2+X X X X X X^2+X X^2+X X^2+X X^2 0 X^2+X X X^2 X^2 X^2 0 X 0 0 X^2+X X 0 X X X 0 0 X^2+X X^2+X X^2 X^2+X X^2+X X^2+X 0 X X^2 X^2 0 X^2 X^2+X X^2 X^2 X^2 0 X 0 0 X^2+X X^2+X X X^2 X^2 X^2 X X^2 X 0 X^2+X 0 X^2 0 0 0 0 X^2 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^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 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 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 0 0 X^2 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 generates a code of length 68 over Z2[X]/(X^3) who´s minimum homogenous weight is 60. Homogenous weight enumerator: w(x)=1x^0+229x^60+60x^61+542x^62+216x^63+855x^64+288x^65+982x^66+432x^67+1102x^68+496x^69+956x^70+312x^71+753x^72+176x^73+392x^74+64x^75+189x^76+4x^77+50x^78+59x^80+18x^82+8x^84+4x^86+3x^88+1x^96 The gray image is a linear code over GF(2) with n=272, k=13 and d=120. This code was found by Heurico 1.16 in 84.5 seconds.