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 1 1 1 1 X^2 X X^2 X^2 X^2 X^2 X^2 X X X^2 1 1 0 1 X^2 1 X^2 1 1 X^2 X 1 0 X X X 1 1 X X^2 X 0 X 0 0 0 0 0 0 X^2 X^2 X X^2+X X 0 0 X^2 X^2+X X^2+X X X X X 0 X X^2+X X 0 X X^2+X X^2 X^2+X X^2 X^2 X^2+X X 0 0 X X^2 X^2 X X X 0 0 X X^2 X^2 X 0 X^2 X^2+X 0 X^2 0 X^2+X X^2 X^2 0 X^2 0 X X^2+X 0 X^2 X^2+X 0 X X^2+X 0 0 X 0 0 0 0 0 0 0 0 0 X^2 X^2+X X^2+X X^2+X X X^2+X X^2+X X X^2 X^2 X^2+X X^2+X 0 0 X X X X^2+X X^2+X X^2+X X^2 X^2 X^2+X X X X^2 X^2 X X X^2 X X^2 X^2 X^2 X^2+X X^2 0 X^2 X 0 X^2 0 X X^2 X^2+X X^2 0 X^2 X^2 X^2+X 0 X 0 X^2+X X^2+X X^2 X^2 0 0 0 X 0 0 X^2 X^2+X X X X X X^2 X^2+X X X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X X^2+X X X^2 X X^2+X X^2+X X X^2+X 0 X^2 0 0 0 X^2+X X^2 X 0 X X^2 X 0 X^2+X X^2 X 0 X^2 0 X^2 X X^2 X X^2+X X X 0 0 0 X^2+X X X^2 0 X X^2 0 X^2+X 0 0 0 0 X 0 X^2+X X^2+X X X^2 X^2+X X^2+X 0 X X 0 X^2 X 0 X^2+X X^2+X X X^2+X X X^2 X^2 X X^2 X^2 0 X^2+X X^2 0 X^2+X X X^2+X X^2 0 X 0 0 0 0 0 X 0 X^2 X^2+X X^2 X 0 X^2 0 X^2 X X^2+X X X^2+X X^2+X 0 0 X^2 X X X^2 0 X^2+X 0 X^2 0 0 0 0 0 X X X^2 X^2+X X X^2+X X^2 X X 0 X 0 X^2+X X^2+X 0 X X^2 X^2 X^2+X X^2 X X^2+X X^2+X X^2 X X^2 X^2 X^2+X 0 X X^2+X 0 0 X X X^2 0 X^2 X^2+X X^2+X X^2 X^2+X X^2 X^2+X 0 X^2 X^2 0 0 X^2 X^2+X X^2+X X 0 0 X X^2+X 0 X^2 0 0 X^2+X X X^2+X generates a code of length 69 over Z2[X]/(X^3) who´s minimum homogenous weight is 59. Homogenous weight enumerator: w(x)=1x^0+64x^59+128x^60+258x^61+277x^62+292x^63+422x^64+462x^65+613x^66+632x^67+648x^68+764x^69+678x^70+560x^71+580x^72+482x^73+366x^74+278x^75+172x^76+168x^77+90x^78+82x^79+75x^80+40x^81+21x^82+10x^83+20x^84+2x^85+2x^86+2x^87+2x^88+1x^94 The gray image is a linear code over GF(2) with n=276, k=13 and d=118. This code was found by Heurico 1.16 in 6.16 seconds.