The generator matrix 1 0 0 1 1 1 X^2+X 1 X 1 1 1 0 X 0 X 1 1 1 1 X^2+X 1 X^2+X X^2+X 1 1 1 0 1 1 0 1 X^2 X 0 1 1 X^2 1 0 1 1 X 1 X^2 1 1 X^2 1 1 0 1 1 1 0 0 X^2 1 0 X 1 X^2+X X^2+X X X 1 1 X X^2 1 1 1 X^2 1 1 1 1 0 X 1 1 X^2+X 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 X^2+1 X X^2+X 1 1 1 1 X^2+X 1 X^2+X X^2 X^2 X+1 1 X X^2+X X^2 1 X^2+X X^2 1 1 1 X^2+1 X+1 1 0 1 X^2+1 1 X X 1 1 X 0 X^2+X X 1 1 X^2 1 1 X^2 1 1 X 1 X X^2 1 X X^2+1 X X^2 1 X^2+X X^2 X^2+1 X^2+1 X 0 X^2+X+1 X 1 X^2+X 0 0 1 1 1 0 1 1 1 X^2+1 0 X^2 1 X^2 1 X^2+X X^2+X X+1 X^2+X X^2+X+1 X+1 X X^2+X X^2+X+1 X X+1 X^2+1 1 X^2+X X X+1 X^2+X+1 1 1 X X^2+1 0 1 X^2+X 0 X^2+1 X^2+1 X+1 1 X 1 X^2+X+1 1 0 1 X^2+X X^2 X 1 1 X^2+X+1 X X X^2+X 1 X X^2+1 1 1 1 0 X+1 X+1 1 X^2 0 X X X^2+X 0 X^2+X X^2 1 1 1 X+1 X^2 X^2+1 0 0 0 X 0 0 X^2 X^2 X^2 X^2+X X X X^2+X X X 0 X^2 X^2+X 0 X^2+X X X X 0 X X^2 X^2 X^2+X X^2+X X^2+X 0 X^2 0 X X^2+X X X X^2+X X^2 0 0 0 X^2+X X 0 X^2+X X^2+X X^2 X^2 0 X X^2+X X^2 X^2 X^2+X X X X^2+X 0 X^2+X 0 X^2 X^2+X X^2+X 0 X^2+X 0 X^2 0 0 0 X X^2 0 X X^2 X^2 X^2+X 0 X^2 0 X 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^2+X X X^2+X X X^2+X X^2+X X^2 0 0 0 0 0 X^2+X X X^2+X X^2+X X^2 X^2 X X^2+X X^2+X 0 X X^2 X 0 X^2+X X^2 X^2 0 X^2 X X X^2+X X^2 0 0 X^2 X X^2 X^2+X X^2+X 0 X^2 X^2+X X^2 0 X^2 X^2 X X^2 X X^2 X X X 0 0 X^2 X^2+X X^2+X X^2+X X X^2 X^2 0 0 0 generates a code of length 83 over Z2[X]/(X^3) who´s minimum homogenous weight is 75. Homogenous weight enumerator: w(x)=1x^0+128x^75+273x^76+450x^77+554x^78+614x^79+689x^80+662x^81+648x^82+572x^83+633x^84+658x^85+517x^86+398x^87+385x^88+344x^89+238x^90+160x^91+78x^92+66x^93+47x^94+24x^95+14x^96+10x^97+12x^98+8x^99+6x^100+2x^101+1x^104 The gray image is a linear code over GF(2) with n=332, k=13 and d=150. This code was found by Heurico 1.16 in 4.45 seconds.