The generator matrix 1 0 0 0 1 1 1 1 1 1 1 X^2 0 0 0 0 1 X^2 1 1 1 1 1 X^2+X X X X 1 0 X^2+X 1 1 1 1 X 1 X^2 1 X 1 X^2+X 1 X^2 1 1 1 X^2 1 1 0 1 1 0 1 1 1 X^2 1 X^2 X^2+X X^2+X 0 1 1 0 1 1 1 1 0 1 0 0 0 0 1 X^2+X+1 1 1 X^2+X 1 1 X^2 1 X^2+X X 1 X+1 X^2+1 X X+1 1 1 1 1 X^2+X X^2+X X X^2 X X^2 X^2+X X+1 1 1 X^2 X^2+X 1 X+1 1 X 1 1 X^2+X X^2 1 X^2 X^2+X+1 1 0 X+1 1 X^2+1 X+1 X^2+X+1 1 X X^2+X 1 0 1 X^2+X X^2+X 0 X^2+X+1 X^2+1 X^2+X 0 0 0 1 0 0 1 0 1 X^2+1 X^2 1 X^2+X+1 X+1 1 0 0 X^2 X^2+X+1 X^2+X X^2+X X+1 X^2+X+1 1 X^2+X 0 X+1 1 X^2+1 1 0 X X^2+X+1 X^2 X^2+X+1 X X^2+X 1 X^2+1 1 1 X 0 X^2+X 0 X X+1 X+1 X^2+1 X^2 X+1 X^2 X^2+X+1 X^2+X X^2+X+1 X^2 X^2 X+1 X X^2 X^2+X+1 X^2+X X+1 1 0 1 X X X+1 0 0 0 0 1 1 X+1 X^2+X+1 X^2+1 X^2 X X^2+X X^2+1 0 X+1 1 1 X X^2+X X+1 X^2 1 X^2+X X^2+X+1 X^2+X+1 X 1 0 0 1 1 X^2+1 1 0 0 X^2+X X^2 X+1 1 X^2 X+1 X+1 X+1 X^2+X+1 1 1 X^2+X X^2+X+1 X^2+1 1 X^2+1 0 X X^2+X X^2+1 X^2+X X+1 X X^2+1 1 X^2+1 1 X^2+X+1 X X X^2+1 X^2 1 X^2 0 0 0 0 0 X X X X 0 0 0 X^2+X X^2 X^2+X X^2+X X^2+X X^2 0 X X^2 X^2+X 0 X^2+X X^2+X X^2 X X X^2+X 0 0 0 X^2 X^2+X X^2+X X^2+X X X^2 X^2 X^2+X 0 0 X^2 0 X^2 X^2+X 0 X X^2 X^2 0 X^2+X X 0 X^2 X X^2 X^2 X X^2 0 X^2+X X^2+X X X^2+X X^2 X X X^2 X^2 0 0 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 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+60x^59+300x^60+656x^61+962x^62+1320x^63+1496x^64+2014x^65+2462x^66+2772x^67+2953x^68+2914x^69+3108x^70+2590x^71+2342x^72+2148x^73+1612x^74+1198x^75+772x^76+448x^77+276x^78+206x^79+53x^80+38x^81+26x^82+10x^83+19x^84+6x^85+2x^86+4x^87 The gray image is a linear code over GF(2) with n=276, k=15 and d=118. This code was found by Heurico 1.16 in 46 seconds.