The generator matrix 1 0 0 0 1 1 1 X 1 X^2+X X 1 X^2 1 1 0 1 1 X^2 1 1 1 X 0 1 1 1 X^2 X 0 1 1 0 1 X^2+X X^2 X^2 1 X 1 1 X 1 X^2+X X^2 1 X 0 1 1 X^2 X^2+X 1 1 X 1 1 1 1 X^2+X 1 1 1 X^2+X 1 0 1 1 1 1 0 X^2+X 1 1 X^2 X 1 1 1 1 0 1 0 1 0 0 X X X^2+X X^2+X X+1 1 1 X^2+X+1 1 X^2+X+1 X+1 0 X^2 1 X 1 X^2 X^2+X 1 X X^2+1 X^2+X X^2+1 1 1 1 1 0 1 0 1 1 X 1 0 X^2+1 X^2 X^2 X+1 1 X^2 X^2+X X^2 1 0 X^2+1 X^2+X 1 X^2+1 X^2+X 0 X^2+1 0 X^2 X 1 X+1 X X^2 X^2 X^2+1 X^2 X^2+X X^2+X+1 0 X^2+X X 1 X+1 X^2 1 1 X^2 X^2+X+1 X+1 X 1 0 0 0 1 0 X X^2+X+1 X^2+X+1 1 X+1 X^2+X X+1 X^2+X X^2+1 X^2+1 X^2 1 X 0 X 0 X^2+X 1 X+1 1 X+1 X+1 1 1 X^2+X X^2 X^2+X X^2+X+1 X^2+X X^2 X^2+1 X^2+X 1 X^2+1 1 X^2+1 X^2+X+1 0 X^2+1 1 1 X+1 1 X+1 X X^2+1 0 X X X^2+1 0 X+1 X^2+1 X^2+1 X^2 X^2+1 X X^2+1 X+1 1 1 X X^2+1 1 X X^2+X 1 X^2 X^2 X^2+1 X+1 0 X^2+1 X^2+X X^2+X X^2+1 X^2 0 0 0 0 1 X+1 X^2+X+1 X X^2+X+1 X^2+X+1 X+1 X^2+X X^2+X 1 0 X^2+X+1 X^2+X X^2+1 X 1 X^2+1 X^2 1 X^2+X+1 X^2+X+1 X^2+X X^2 X+1 X^2+X X^2+1 X^2+X X+1 1 1 1 0 X^2 1 X X^2+X X^2+1 X^2 1 X X+1 1 X^2+1 X^2 X X^2+X X^2+X+1 1 X^2+X+1 X^2+1 1 1 X^2 X X+1 X^2+X 1 1 X X 1 X^2 1 X^2+X+1 X^2+X+1 X^2+X X^2+X X^2+X 0 0 X+1 X^2+X X^2+X+1 X^2+X X+1 0 0 X^2+X 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 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+113x^74+206x^75+519x^76+574x^77+776x^78+562x^79+689x^80+534x^81+712x^82+598x^83+586x^84+432x^85+510x^86+320x^87+350x^88+176x^89+203x^90+130x^91+87x^92+34x^93+50x^94+6x^95+8x^96+10x^97+4x^98+2x^99 The gray image is a linear code over GF(2) with n=328, k=13 and d=148. This code was found by Heurico 1.16 in 3.89 seconds.