The generator matrix 1 0 0 0 1 1 1 X^2 X 1 1 0 X^2 1 1 1 X^2+X X^2+X X^2 1 1 1 1 X^2+X 1 X^2 X^2+X 1 1 0 1 1 1 X 1 0 X^2+X 1 0 1 1 X^2+X X 1 X^2 1 X^2+X 1 0 0 1 0 1 X^2 1 X X^2+X 1 1 1 X^2+X 1 1 1 1 1 1 1 X 1 X 0 1 1 1 X^2 X^2+X 1 1 X^2+X X^2 0 1 1 0 1 0 0 1 X^2 1 0 1 1 X^2 1 1 X 1 X^2+X 1 1 X X+1 X^2+X X^2+X X^2+X+1 X X^2+1 X^2+X 1 1 X 1 0 X^2+X+1 1 0 X^2+1 X^2+X X X^2+X+1 1 X+1 X^2 1 1 0 X^2+X X 0 X+1 1 1 0 X X^2 1 X^2+X 1 X^2+X X^2 0 X^2+X+1 X^2+X X+1 0 0 X+1 X^2+X X^2+1 1 X X^2+1 1 1 X^2+X 1 X+1 X X^2 X^2+X+1 0 X^2 1 X^2 1 0 0 0 1 0 X 0 X^2+X 1 X^2 X^2+X+1 1 X^2+X+1 X^2+X+1 1 X^2+1 X+1 1 X^2 1 0 X^2+X 0 X 1 X^2+1 X^2 X^2+X+1 1 X+1 0 X^2+1 1 0 0 X^2+X 1 X X^2+1 X^2+1 X^2 X X X^2+1 X+1 1 1 1 X^2+X+1 X+1 X^2+X X^2+1 1 X X X^2+1 X^2 0 X^2 X^2+X X^2+X 1 X^2+X X^2+1 0 X 0 X^2+X+1 0 X X 0 X+1 X^2+X+1 X^2 X^2+1 1 1 X^2+X+1 X+1 0 X X^2 1 1 0 0 0 1 X 1 X+1 1 1 X^2+1 X^2+X X^2+X X+1 X+1 X^2 0 X^2+1 X^2+X+1 0 X^2+X X^2+X X+1 X^2+X+1 X^2+X+1 X^2+X+1 1 X^2 X 1 X X+1 0 X+1 1 X^2 1 1 X^2+1 1 X+1 X+1 0 X X X 1 X X X^2 0 X^2+1 X^2+X+1 X^2 X^2+1 0 X^2 1 X^2+X X^2+X+1 X^2+X 0 X X^2 X^2+X 0 0 X^2+1 X^2+X+1 1 1 X^2+X+1 X^2+X 1 X^2+1 X^2+X 0 X X+1 0 1 0 1 X^2+X+1 1 0 0 0 0 X^2 0 X^2 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 0 generates a code of length 84 over Z2[X]/(X^3) who´s minimum homogenous weight is 76. Homogenous weight enumerator: w(x)=1x^0+50x^76+340x^77+455x^78+606x^79+530x^80+658x^81+751x^82+716x^83+649x^84+644x^85+506x^86+550x^87+344x^88+360x^89+217x^90+238x^91+185x^92+184x^93+103x^94+28x^95+31x^96+22x^97+14x^98+6x^99+2x^100+2x^102 The gray image is a linear code over GF(2) with n=336, k=13 and d=152. This code was found by Heurico 1.11 in 1.55 seconds.