The generator matrix 1 0 0 1 1 1 X 1 1 X^2+X 1 1 X X^2+X X 0 1 1 1 1 X^2+X X^2+X 1 1 1 1 0 0 1 X^2 1 X^2+X 0 1 1 X X 1 1 X^2+X 1 1 1 X^2 1 1 1 1 X^2 1 1 X X^2+X 1 X^2+X 1 X^2 0 X^2+X 1 1 1 X 1 1 1 1 1 1 0 1 0 X 1 X^2+X+1 1 X^2+X 0 X^2 1 X+1 X^2+X 1 1 1 X^2+X+1 X^2+X 0 X^2+1 1 1 X^2+1 X 0 X+1 1 0 X^2+X 1 X^2 X^2+X 1 X^2+1 X^2+1 1 0 X+1 X+1 1 X^2+X+1 X^2+X X X^2+X 0 X+1 X X+1 1 X^2 X^2+1 1 X^2+X X^2+X+1 1 X^2+X 1 X^2+X 1 X^2+X X^2 X^2+X+1 1 X^2 X X^2+1 X^2+X+1 X^2+X 1 0 0 1 1 X^2+X+1 X^2+X 1 X+1 X^2+X 1 1 0 1 X+1 X X+1 1 X^2 X^2+X+1 X^2+X 0 X 0 X X^2+1 X^2+X+1 X+1 1 X^2+X+1 1 X^2+X 1 X X^2+1 X^2+X+1 1 1 0 X X^2+X+1 X X^2 X^2+X 1 1 X^2 0 X^2+1 X X^2+X+1 X^2+X+1 X^2 1 X X^2+1 X^2+X+1 1 1 X^2+1 X^2 1 X^2+1 X+1 X^2+X 1 X^2+1 X+1 1 1 0 0 0 X^2 0 0 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 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 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 0 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 X^2 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 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 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 0 X^2 X^2 0 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 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 0 0 X^2 0 0 0 0 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 generates a code of length 69 over Z2[X]/(X^3) who´s minimum homogenous weight is 61. Homogenous weight enumerator: w(x)=1x^0+80x^61+233x^62+414x^63+457x^64+586x^65+687x^66+690x^67+679x^68+706x^69+847x^70+584x^71+526x^72+560x^73+382x^74+300x^75+172x^76+100x^77+67x^78+50x^79+16x^80+14x^81+19x^82+10x^83+5x^84+2x^85+5x^86 The gray image is a linear code over GF(2) with n=276, k=13 and d=122. This code was found by Heurico 1.16 in 3.46 seconds.