The generator matrix 1 0 0 0 1 1 1 1 1 1 1 X^2 0 X^2+X X^2 0 0 0 X^2+X 1 1 X 1 0 1 1 X 1 1 1 X^2 1 1 1 0 X^2+X X^2 X^2+X X 1 1 1 1 1 X 1 1 X^2+X 0 1 1 1 X^2 0 1 1 1 1 X 1 1 X X^2+X 1 1 X X 1 X X X^2 1 1 1 0 1 0 0 0 0 1 X^2+X+1 1 1 X^2+X 1 1 X 1 0 1 X^2 0 X^2 X+1 1 X^2+X 1 X^2+X+1 X 1 X^2+1 1 X+1 1 X^2+1 X 0 X X X 1 1 1 X^2 X^2+X+1 X^2 X+1 1 X X^2+X+1 1 1 X+1 X^2+1 X 1 X^2+X X 0 X^2+X X^2+X 1 X^2+X+1 0 1 X X^2+1 0 1 0 X^2+X X^2+X X^2+X 1 X^2+1 X 0 0 0 1 0 0 1 0 1 X^2+1 X^2 1 X^2+X+1 X+1 1 X^2 X 1 1 1 X^2+X X^2+X+1 X^2+X X X^2+X+1 X^2+X X+1 1 1 X+1 X X^2+X 0 X^2+1 X^2 1 1 X^2 X^2+X+1 X^2+X+1 X 0 0 X+1 X^2+X+1 0 1 X^2 X^2+X X+1 X^2 X+1 0 X X X^2 X^2+1 X^2 X^2+X X^2+1 0 X^2+X+1 X X^2 1 X+1 X^2+X+1 1 X+1 1 1 X+1 X^2+X X^2+X 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^2+X+1 1 1 X^2 1 X^2+X X^2+X X+1 0 X^2+1 X X^2+1 X X+1 X+1 0 X^2 1 1 1 X^2+X+1 0 X^2+X+1 1 X^2+1 X^2 X^2 X^2+1 X^2+X+1 0 X^2+X X^2+X+1 0 0 X^2+X X^2+X+1 X^2+1 X+1 X 1 1 X^2+X+1 X+1 1 X X^2+X X^2+X X^2+X+1 1 1 X^2 0 X^2+X X^2+1 X^2+1 1 X^2+X 1 1 X^2+1 X^2 0 0 0 0 X X X X 0 0 0 X^2+X X^2 X^2+X X^2+X X X^2 X^2+X 0 0 X^2+X 0 X X^2 X^2+X 0 X X X^2 X^2 0 0 X^2 X^2 X 0 0 X^2 X X X^2 X^2 X X 0 X^2+X X^2+X X X^2 X X^2 X^2+X X^2 X^2 X X^2 0 X X^2 X^2+X X^2 X X^2+X 0 X X^2 X 0 X 0 0 X^2 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 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 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 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 0 X^2 0 0 generates a code of length 74 over Z2[X]/(X^3) who´s minimum homogenous weight is 64. Homogenous weight enumerator: w(x)=1x^0+83x^64+402x^65+684x^66+1054x^67+1251x^68+1848x^69+1858x^70+2502x^71+2478x^72+2918x^73+2590x^74+2976x^75+2634x^76+2604x^77+1980x^78+1666x^79+1044x^80+924x^81+504x^82+352x^83+171x^84+122x^85+50x^86+24x^87+18x^88+12x^89+14x^90+2x^91+2x^93 The gray image is a linear code over GF(2) with n=296, k=15 and d=128. This code was found by Heurico 1.16 in 50.8 seconds.