The generator matrix 1 0 0 1 1 1 X X^3+X 1 1 1 X^3+X^2 X^2+X 1 1 X^2+X 1 0 1 X 1 1 1 1 1 X^3+X X^2+X 1 X^3+X 1 X 1 X^2 1 X^3+X^2 X 1 X^2 1 X^2 1 X^3+X^2 1 X^3 X^2 1 1 0 1 1 1 1 X^3 1 X^2+X X^3 1 X X^3 1 1 X^2 X X 1 X^3+X X 1 X^3+X^2 X^3 1 1 X^3+X 1 1 X^3 1 1 X^3+X^2 1 X^3+X 1 0 1 0 0 X^2+1 X+1 1 X^3 0 X^3 X^3+1 1 1 X+1 X^2 X^3+X X^3+X+1 1 X^3+X^2+X 1 X^3+X^2+1 X^3+X^2+X X^2+1 X^3+X^2+X+1 X 0 1 X^3+X^2+X 1 X^3+X^2+X+1 1 X^2 1 X^2+X 1 X^2 X^2+X 1 X^2 X^3+X^2+X X^2+X+1 X^3 X^2+1 1 1 X^3+X X^3+X^2+1 X^2+X X^3+X X^3+X^2+1 X^3+X^2+X+1 X^2+X+1 X^3+X X^3+X 1 1 X+1 1 X X^3+X^2+1 X^3+1 1 0 X^3+X^2+X X^3+X^2+1 X^2+X 1 X^3+X^2+X+1 1 1 X^2+X X+1 1 X^3+X^2+1 X^3 1 X^2 X^3+X 1 X^2+1 1 0 0 0 1 1 1 0 X^2+1 1 X X^3+X^2+X+1 X^2+X X+1 X^3+X^2+X 1 X^3+X+1 1 X^3+X+1 X^2+X X^3+X^2 1 X^3+X^2 X^2+X X+1 X^3+X^2 X^2+1 1 X^3+X^2 X^2 X^2+X+1 X^3+X+1 X^3+X X^3+X^2+1 X^3+X^2+X+1 X^3+1 X^3+1 1 X^2+X X^2 X^3 1 X^3+X^2+1 1 X^3+X^2 X X X+1 X^2+1 1 X^3+X^2 X^2+X+1 X^3+X X^3+X+1 1 X+1 X^3+X^2+X+1 1 X^2 X 1 X^2+X X^2 X^2 1 1 X^3 1 X^3+X X^3+X^2+X 0 X^3+1 0 X^3 1 X^3+X X^3+X^2+X X^2+1 X^2 X^3+X^2+X X^3+X^2+1 X^3+X X^2 0 0 0 0 X X^3+X X^3 X^3+X X^3+X X^3+X X X^3+X^2+X X^3 X X^2 X^2 X^2+X X^2+X X^3+X X^3+X^2 X^2 X^2 X 0 X^2+X X^2 X^3 0 X^3+X^2+X X^3+X^2+X 0 X^3+X^2 X^3+X^2 X X^2+X 0 X^3+X^2+X 0 X^3+X^2+X X^2+X X^3+X^2 X^3+X X^3+X^2+X X^2+X X^3 X^2+X X^3+X X^2+X X^3 X X^3+X X^3+X X^3+X^2 X^3+X^2+X X^2+X X^3+X^2 X^3+X 0 0 X X^2 X^3+X X^2 X^3+X^2 0 X^3 X^3+X X X^3+X^2 X^3+X X^3+X^2 0 X^3+X^2 X^2+X X^2+X X^3+X^2+X X^3+X^2+X X^2+X X^2 X^3+X^2 X^3+X^2 X^2 X^3 generates a code of length 82 over Z2[X]/(X^4) who´s minimum homogenous weight is 75. Homogenous weight enumerator: w(x)=1x^0+84x^75+673x^76+1448x^77+2496x^78+2988x^79+3535x^80+3904x^81+3624x^82+3660x^83+3226x^84+2580x^85+1912x^86+1160x^87+770x^88+300x^89+190x^90+64x^91+55x^92+44x^93+24x^94+12x^95+3x^96+12x^97+2x^98+1x^104 The gray image is a linear code over GF(2) with n=656, k=15 and d=300. This code was found by Heurico 1.16 in 17.3 seconds.