The generator matrix 1 0 0 1 1 1 X^2+X 1 X 1 1 1 0 X 0 X 0 1 1 1 1 1 1 1 1 0 X^2 X^2 X X^2+X 1 1 0 X^2 1 1 X^2 1 X 1 1 X X X 1 1 0 1 X^2 1 0 1 1 1 1 0 0 1 1 1 X^2+X X 1 1 1 1 1 X^2+X 1 0 1 1 0 1 X^2 X X^2 1 X X^2 1 1 0 1 0 0 1 X+1 1 X^2+X 0 X+1 X^2+X 1 1 1 X^2+X 1 1 1 X^2+1 X^2 X^2+X X+1 X+1 0 X^2 1 1 X 1 X^2+X X+1 X 1 1 X^2+X X 1 1 0 X^2+X+1 0 X^2 1 1 X+1 X^2+X X^2+X 0 1 X X^2+X 0 X^2 X^2+1 0 1 1 X^2+X X^2+X+1 0 X^2 1 0 X^2+X 1 X^2+X+1 X^2+X X^2+X X^2+X+1 1 X^2 X^2+X+1 1 X^2+X+1 X^2+X 1 1 X^2+X+1 1 1 X X^2 0 0 1 1 1 0 1 1 1 X^2+1 0 X^2 1 X^2 1 X+1 X^2+X X X^2+X+1 X X+1 0 X^2+1 1 X^2+X X^2 X^2+X+1 1 X^2+X+1 1 X+1 X^2+X 0 X^2+1 X+1 X^2 X^2 X^2+X+1 1 X^2 X^2+1 1 X^2+1 X^2 X+1 0 1 1 X^2+X 0 1 X^2+X 0 X X^2+X X X+1 X^2+X X^2+1 X+1 1 X^2+X+1 X^2+X+1 X^2+X X^2+X+1 X^2+1 1 1 X+1 X^2+X+1 0 0 X^2+1 X^2+X 1 1 X^2 0 X+1 X^2+X+1 X^2+1 X^2 0 0 0 X 0 0 X^2 X^2 X^2 X^2+X X X X^2+X X X 0 0 X^2 X^2+X X^2+X X X^2+X 0 0 0 X^2+X X X X^2+X X X X^2+X X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X X^2 X^2+X 0 0 0 X^2+X X^2+X X^2+X 0 X^2 0 X^2 0 X X^2+X X^2 X^2+X X X^2+X X^2 X 0 X^2 X X^2 0 0 X X^2+X X X 0 0 0 X X^2+X X 0 X^2 X^2+X 0 0 0 0 X X^2 X X^2+X X^2+X X^2 X X^2+X 0 X 0 X X^2 0 X^2 X^2+X 0 X^2+X X X^2+X 0 X X^2 X^2+X 0 X^2+X X X^2 X^2+X 0 X^2 X^2+X X^2+X X^2 0 X X^2 X^2 X^2 X^2 0 X 0 X X X^2 X^2+X 0 X^2+X X^2 X^2 X^2 X^2+X 0 X^2+X X X^2 0 0 X^2+X X^2+X X X^2 X X^2 0 0 0 X^2 X X^2 X^2 X^2+X X X X X^2+X 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+144x^74+264x^75+393x^76+572x^77+642x^78+624x^79+670x^80+660x^81+690x^82+636x^83+539x^84+608x^85+422x^86+352x^87+315x^88+244x^89+130x^90+100x^91+84x^92+28x^93+32x^94+8x^95+6x^96+14x^98+8x^100+4x^102+2x^106 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 4.8 seconds.