The generator matrix 1 0 0 0 1 1 1 X X^2 1 1 0 X^2 1 1 1 X^2+X 1 X^2+X 1 1 1 X^2 1 X X^2 1 1 1 0 1 X 0 1 X^2+X 1 1 1 0 0 1 X^2+X X^2+X 1 1 1 X^2+X 1 X^2+X 1 X^2 1 1 1 1 1 1 X 1 1 1 0 1 X^2 0 1 X^2 X 1 0 1 X^2+X X^2 X^2+X X X^2+X 1 X^2 X^2 1 1 1 0 1 0 0 1 X^2 1 1 0 1 X^2 1 1 X 1 X^2+X 1 X^2+X+1 1 X+1 0 X^2+X 0 X+1 0 X^2+X X^2 X+1 0 X^2+X X^2+1 1 1 X+1 1 X X^2+X+1 0 1 X^2+X X^2+X 1 X 1 X^2 X^2+1 1 X 0 1 1 X^2+X X X X+1 X^2 X^2+1 1 X^2+X+1 X^2+X X^2+X+1 1 X 0 1 1 X^2 X X X^2+X X^2+X+1 1 1 1 X^2 X^2+X X^2 1 1 0 1 0 0 0 1 0 X 0 X^2+X X^2 1 X^2+X+1 1 X^2+X+1 X^2+X+1 1 X^2+1 X+1 X^2+X+1 X^2 X^2+X X+1 X^2 X^2 1 X^2+X X^2+X 1 X+1 1 X+1 1 X^2 X^2+X+1 X^2+X X 1 1 X^2+1 X^2+1 0 1 X^2+X 0 1 X^2 X^2+X+1 X X^2+1 X^2+X+1 X X X X^2+X X+1 X^2+1 X+1 X 0 X+1 X 0 X^2+X+1 X^2+X 0 1 X^2+X+1 X^2+X+1 0 1 X+1 X X^2 X^2+X X^2+1 X^2+X+1 1 1 X^2+X X^2+X X^2+X+1 X^2+X+1 X+1 0 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 X 0 X X^2+X+1 0 X^2+X X^2+X+1 1 1 1 X+1 X^2+X+1 X^2+X+1 X^2+X X^2+X+1 1 1 X^2+X 0 X^2+X 1 X^2+X X^2 X^2+X+1 X^2+X+1 X^2+X+1 X+1 X^2+X 0 X X+1 1 X^2+X X^2+X+1 X^2+X X^2+X X^2+X 0 X^2+1 X^2+1 X+1 X X^2+X+1 X^2+X+1 X X X^2+X X^2+X+1 X 1 X^2+X 1 1 X^2 X^2+X+1 X+1 1 X+1 0 X^2+X 1 X^2+1 0 X^2 0 0 0 0 0 X^2 0 X^2 0 0 0 X^2 X^2 0 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 X^2 X^2 0 0 0 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 generates a code of length 82 over Z2[X]/(X^3) who´s minimum homogenous weight is 74. Homogenous weight enumerator: w(x)=1x^0+62x^74+306x^75+554x^76+532x^77+669x^78+562x^79+679x^80+664x^81+685x^82+530x^83+603x^84+500x^85+467x^86+342x^87+286x^88+236x^89+206x^90+94x^91+105x^92+42x^93+22x^94+20x^95+12x^96+8x^97+1x^98+2x^99+2x^101 The gray image is a linear code over GF(2) with n=328, k=13 and d=148. This code was found by Heurico 1.11 in 1.5 seconds.