The generator matrix 1 0 0 0 1 1 1 X 1 X^2+X 1 X^3+X 1 1 X^3+X^2 X^3+X^2+X X^2+X X^3 1 1 1 1 X^2 X^3 1 X^3+X 1 X^3 X^3+X^2 0 1 1 0 1 1 1 1 X^3+X^2+X 1 X^2+X X^2+X 1 1 1 X^3 1 X X^3+X^2 1 1 1 1 X X^3 X^2+X 1 X^3 1 1 X^3+X^2 1 1 X^3+X X^3 1 1 1 X^2+X X^2 1 1 1 X^3+X 1 1 X^2 1 1 X^3+X^2 1 1 X 1 0 1 0 0 X^3 X^3+X^2+1 X^3+X+1 1 X^2 X^2 X^2 1 X^2+X+1 X^2+1 1 X^2+X 1 X^3+X^2+X 1 X^3+X^2+X+1 X^3+X X^2+1 X^2+X 1 X^3+X^2+X 1 X^3 X^3 0 1 X^2+X X^3+1 1 X^3+X+1 X^3+1 X^2 X^2+X+1 1 X^2 1 1 X^3+X X+1 X^3+X^2+X X^3+X^2 X^2+1 X^2+X X^2+X 0 X^3+X^2+X X^3+X^2+1 X^3 0 X 1 X^3 1 0 X^2+X+1 1 X^3+X^2+X+1 X^3+X 1 1 X^2 1 X^3+X X^2 1 X^2+X X^3+X^2 X^2+X 1 X^3 X 1 X^3+X^2+X X^3+X^2+X+1 1 X^3+X^2+1 X^3+1 0 X^3+X^2+X 0 0 1 0 X^3+X^2 X^3 X^2 X^2 1 1 X^3+X+1 X^3+X+1 X^3+1 X+1 X^2+X+1 1 X^2+X+1 1 X+1 0 X^3+X^2+1 X^2+X+1 X^3+X^2+X X^3+X^2+X X^3 X X X^3+X 1 1 X^3+X^2+X+1 X^3 X^3+1 X^2+1 X^2+X X^3+X^2+X+1 X^3+X^2+X+1 X^2+X 0 1 X^2+X X^3+X^2+X+1 X^2+X+1 0 1 X^2+X+1 X^2 1 1 1 X^2+X X^3+X 1 1 X^2+1 0 X X^3+X^2+1 X^2 X^3+1 X^3+X^2+X+1 X^2+X X^3+X X^2+1 X^2 X^2 X^3 X^2+X X^3+X^2+X+1 X^2+1 X^3+X^2+X+1 X^3+X+1 1 X^2+1 1 X^3+1 X+1 X^2+X X^3 X^3+1 X^3+X 1 X^3+X^2+1 0 0 0 1 X^2+X+1 X^3+X^2+X+1 X^3 X+1 X^3+X+1 X^3+X^2+X+1 0 X^3+X^2+1 X^3+X^2+X X^3+X^2+1 X^2+X 0 X 1 X^3+X+1 X X^3+X X^2 1 0 X^3 X^2+X+1 X+1 1 X+1 X^2+1 X^3+X^2+X+1 X^2+1 X^3+X^2+X+1 X^3+X^2 X^3+X^2 1 X^3+X+1 X^2+X X^3+X^2+1 X X^3 0 1 X^3+X X^2+1 X^3+X 1 X^2 X^3+1 X^2+1 1 X^2 X X^2+X X^2+1 X^2+X X X X^3 X^3+X^2+X X^2+X X^2+X+1 X^3+1 X^3+X^2 X X^2+X X^2+1 1 X^2+X+1 0 X+1 X^2+1 X+1 X^2+1 X^3+X+1 X X X^3+X+1 X^2+X X^2+X X^3+X^2+X X^3+X^2+X X generates a code of length 83 over Z2[X]/(X^4) who´s minimum homogenous weight is 76. Homogenous weight enumerator: w(x)=1x^0+452x^76+1738x^77+3252x^78+4140x^79+6004x^80+6320x^81+7669x^82+7444x^83+7596x^84+6168x^85+5502x^86+3616x^87+2664x^88+1460x^89+821x^90+360x^91+184x^92+98x^93+24x^94+8x^95+3x^96+8x^97+4x^98 The gray image is a linear code over GF(2) with n=664, k=16 and d=304. This code was found by Heurico 1.16 in 45.8 seconds.