The generator matrix 1 0 0 0 0 1 1 1 0 1 X^2 1 X^2 1 X^2+X 1 0 1 0 1 X^2+X X 1 1 1 1 X X^2+X X^2 X^2+X 1 X^2+X 1 1 1 1 1 0 1 1 1 X^2+X 1 1 1 X^2+X 0 1 X X^2+X 1 0 0 1 X^2 X^2+X 1 X 1 1 X 1 X^2 X^2+X 1 X 1 1 X^2+X 1 1 1 X^2 0 X^2+X 0 0 X^2 1 1 X 1 X^2+X 1 0 1 0 0 0 0 0 X^2 X^2 1 1 1 1 1 1 X+1 X^2+X X^2+X 1 X 1 1 X X^2 X^2+1 X^2+1 0 1 X X^2 X^2+X 1 1 X^2+1 X^2+X X^2+X+1 X^2 1 1 1 X^2+X 1 0 X^2+X X^2+1 X^2 X X^2+X X 1 X^2+1 X^2 X^2+X X^2+X+1 0 1 X+1 0 X^2 0 X X^2+1 X X X+1 1 X+1 X^2+X+1 X^2+X X^2+X+1 X X+1 1 1 1 1 1 1 X^2+X+1 0 1 X^2+1 0 X^2 0 0 1 0 0 X^2 1 X^2+1 1 0 1 X+1 X^2+X+1 X^2+1 0 X 1 X^2+X X^2+X X+1 1 1 1 X 1 X^2+1 X^2+X X 1 X^2 X^2 X^2 0 0 X^2 X^2+X+1 X^2+1 X+1 X+1 X^2+1 X^2+X+1 X^2+X X X X^2+X+1 1 1 X^2 X^2+X X^2 X^2 1 X^2 X+1 1 X^2 X^2+X X^2 X^2+1 X^2+X 1 1 1 1 X^2+X+1 X X X^2 1 0 X^2 1 X+1 X^2+1 X^2+X X^2+1 X^2+X+1 X^2 1 X^2+X+1 1 0 1 X^2 0 0 0 1 0 X^2+1 1 0 1 X^2 X^2+1 X+1 X^2 X^2+X X^2+1 X^2+X+1 X^2+X 0 0 X^2 X X^2+X+1 1 1 0 X^2+1 1 X+1 X^2+X+1 1 X^2 X^2+X X^2+X+1 X X^2+X 0 X^2 X X X^2 X^2+X+1 X^2+1 1 X X+1 0 X+1 X+1 0 X 1 X^2+X+1 1 X^2 X+1 X^2+1 X^2+X 1 X^2+X X^2 X^2+1 X^2+X+1 X^2 X^2+X X^2+1 1 X X+1 X^2 X^2 1 X 1 X^2 X+1 X^2 X X X^2 X X+1 X^2+X+1 X^2+X+1 X^2 0 0 0 0 1 1 X^2 1 1 X^2+1 X^2 1 X+1 0 1 0 X^2+1 X^2+X+1 X^2+1 X^2+X X X+1 X^2+X+1 X^2+X X+1 X^2+X X^2+X+1 X^2+X X^2+X 0 0 X+1 X^2+X+1 X^2 X^2+1 0 X 1 X+1 X^2 X^2+X X^2+1 0 1 0 X+1 X^2 X^2+X+1 1 1 X^2+X+1 X^2+1 X 1 X X 1 X X X^2+X+1 X^2 1 0 X^2+1 0 X^2+X X X X+1 X+1 X+1 1 X^2+X X 1 0 X+1 X^2+X+1 X^2+X 0 1 X^2+1 0 X generates a code of length 84 over Z2[X]/(X^3) who´s minimum homogenous weight is 74. Homogenous weight enumerator: w(x)=1x^0+120x^74+474x^75+851x^76+1222x^77+1361x^78+1842x^79+2108x^80+2250x^81+2418x^82+2766x^83+2426x^84+2620x^85+2351x^86+2374x^87+1951x^88+1678x^89+1234x^90+1088x^91+639x^92+388x^93+286x^94+130x^95+82x^96+48x^97+30x^98+12x^99+6x^100+2x^101+8x^102+2x^103 The gray image is a linear code over GF(2) with n=336, k=15 and d=148. This code was found by Heurico 1.16 in 53.2 seconds.