The generator matrix 1 0 1 1 1 X^2+X 1 1 0 1 1 X^2+X 0 1 1 X^2+X 1 1 X 1 1 1 1 0 1 1 0 X^2+X 1 1 1 1 0 1 X^2+X 1 0 1 X^2 X^2+X 1 1 1 1 1 X^2+X 1 1 1 0 0 1 1 1 X^2 1 1 1 0 1 1 1 X X^2 1 X^2+X 1 1 X^2+X X^2 X^2+X X^2+X 1 X 1 1 X 0 1 1 1 1 1 1 0 1 X+1 X^2+X 1 1 0 X+1 1 X^2+X X^2+1 1 1 X^2+X X+1 1 X^2+1 0 1 X^2 X+1 X^2+X+1 X^2+X 1 X^2+1 0 1 1 X^2+X X^2+1 X^2+X X^2+1 1 X+1 1 0 1 0 1 1 1 0 X+1 X X^2+1 1 X^2+X X+1 0 1 1 X+1 X^2+X+1 X^2+X 1 X^2+X+1 X^2+1 X^2+X 1 X X^2+1 X^2 1 1 X+1 1 0 X^2+X+1 1 1 1 1 X^2+X+1 1 0 X^2+X 1 1 X^2+1 X+1 X+1 X+1 0 X^2+X 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 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 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 0 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 0 X^2 0 X^2 0 0 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 0 0 0 0 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 0 0 0 X^2 0 X^2 0 X^2 0 0 0 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 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+89x^74+48x^75+189x^76+280x^77+216x^78+600x^79+235x^80+1032x^81+236x^82+1112x^83+216x^84+1112x^85+205x^86+1032x^87+206x^88+600x^89+186x^90+280x^91+141x^92+48x^93+63x^94+15x^96+12x^98+11x^100+11x^102+6x^104+5x^106+2x^108+1x^110+1x^112+1x^116 The gray image is a linear code over GF(2) with n=336, k=13 and d=148. This code was found by Heurico 1.16 in 33.5 seconds.