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 X 0 1 1 X 0 1 X 0 X 1 0 1 X 0 1 0 X 1 1 1 1 X 1 1 1 X 0 0 0 X 1 1 1 1 1 X X 1 1 1 1 1 0 0 1 X X 0 X 0 X^2+X 0 X^2+X 0 X^2+X 0 X^2+X 0 X^2+X X^2+X X^2 0 X^2+X X X^2 X^2+X X^2+X 0 X 0 X^2 0 0 X^2+X X X^2+X X X^2+X X X^2 X^2+X X X^2+X X X X^2+X X^2+X X 0 X X^2+X X^2+X 0 X^2+X 0 X^2+X 0 X 0 X^2+X X X X X^2+X X^2 X^2 0 X X^2+X X^2 X X^2+X 0 0 0 X^2+X X X X^2+X 0 X^2+X 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 X^2 0 0 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 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 0 0 0 0 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 X^2 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 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 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 0 X^2 0 X^2 0 generates a code of length 74 over Z2[X]/(X^3) who´s minimum homogenous weight is 60. Homogenous weight enumerator: w(x)=1x^0+141x^60+56x^62+4x^63+476x^64+60x^65+314x^66+268x^67+830x^68+692x^69+758x^70+1288x^71+1140x^72+1784x^73+840x^74+1784x^75+1147x^76+1288x^77+724x^78+692x^79+799x^80+268x^81+314x^82+60x^83+391x^84+4x^85+62x^86+131x^88+4x^90+48x^92+12x^96+3x^100+1x^104 The gray image is a linear code over GF(2) with n=296, k=14 and d=120. This code was found by Heurico 1.16 in 28 seconds.