The generator matrix 1 0 0 1 1 1 0 X^3+X^2 X^3+X^2 X^3+X^2 1 1 1 1 X^2+X 1 X^2+X 1 1 1 X 1 1 X X^3+X^2+X X^2+X 1 1 X^3+X 1 1 X^3+X 1 X^3+X^2+X 1 1 1 X^3+X 1 X 1 1 1 X^2 1 1 0 X^3 1 0 X^2+X 1 1 0 1 X^2 1 1 1 1 1 1 X^3 X X X^3 X^2+X 1 1 1 1 X 1 X^3+X^2+X 1 1 1 1 1 1 0 1 0 1 0 0 X^2+1 X^3+X^2+1 1 X 1 1 X^3+X^2 X^2 X^3+X^2+1 X^3+X^2+1 X^3+X^2 X+1 1 X^2+X X^3+X^2+X+1 X^3+X 1 X X^2+X 1 1 X X+1 X+1 1 1 X^3+X^2+1 1 X^3+X X^3+X X^2+X X^3+X+1 0 X^3 0 1 X^2 X^2+X+1 X^2 1 X X^3+X^2+X+1 1 1 X^3+X^2+X+1 X^3+X^2+X 1 1 X^2+X+1 X^2+X X^3+X^2+1 X^3 X^3+X^2+X X+1 X^2+X X^3+X X^2+1 X^2 1 1 1 1 0 0 X^2+1 X^3+X^2 X^2+X 1 X^2+X+1 1 X^3+1 1 X^3+X^2 0 X^2 X^3+X^2+X+1 1 X^3 0 0 1 X+1 X^2+X+1 X^2 X^2+X+1 1 X X^3+1 X X^3+X^2+1 1 X^2+X 1 X^2+X X^2+1 1 X+1 X^3+X X^3+X X^2 X^3+X^2+X+1 X^2 X^3+X+1 1 1 0 X+1 X^2+X+1 0 X^3 X 1 X+1 X^3+X+1 X^3+X^2+X 1 X^2+X+1 X^3+1 X^3 X^2+1 X^2+1 X^3 1 X^2 X^3+X^2+1 X+1 X^3+1 1 X^3+X^2+X X^2+X X^2+X+1 1 1 1 0 X^3+X X^3+X^2+1 X^3+X^2+X+1 X^2+1 X+1 X^2+X X^2+1 X^3+X^2 X^3 1 X^3+X+1 X^2+X X^3+X^2 X^3+X^2 X^3+X^2+1 X^3+X^2+1 X^3 1 X^2+X+1 X^3+X^2 X^3+X X X^3+X^2+X+1 X^2+1 X^3 0 0 0 X^2 X^2 0 X^2 X^3+X^2 X^2 X^3 X^2 0 X^3 X^3+X^2 X^3+X^2 0 X^2 X^2 0 0 X^3 X^3+X^2 0 X^2 X^3 X^3 X^3+X^2 X^3 X^3+X^2 0 X^3+X^2 X^3 X^2 X^3+X^2 X^3+X^2 X^2 0 X^2 X^3 X^3+X^2 X^2 0 X^3+X^2 X^3+X^2 0 X^2 X^3+X^2 X^3 X^3+X^2 X^2 X^2 X^3+X^2 X^3+X^2 X^3 X^2 X^2 X^2 X^3+X^2 X^3+X^2 X^2 0 X^3 0 0 X^3 X^2 X^3 X^3+X^2 0 X^3+X^2 X^3 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^2 X^3 X^2 X^3+X^2 0 X^3+X^2 X^3 generates a code of length 82 over Z2[X]/(X^4) who´s minimum homogenous weight is 76. Homogenous weight enumerator: w(x)=1x^0+87x^76+836x^77+1296x^78+1612x^79+1861x^80+2156x^81+1802x^82+1748x^83+1518x^84+1264x^85+714x^86+660x^87+399x^88+200x^89+84x^90+88x^91+23x^92+8x^93+10x^94+4x^95+5x^96+6x^98+2x^100 The gray image is a linear code over GF(2) with n=656, k=14 and d=304. This code was found by Heurico 1.16 in 8.5 seconds.