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 1 0 1 1 X^3+X^2 1 1 1 1 1 1 X^3+X 0 X^3+X^2+X 0 1 1 1 1 1 1 X^3+X^2+X 1 X^3+X^2+X 1 X^3 X^2 X^3+X^2 1 X^2 X^3+X 1 1 X^3+X^2+X 1 X^3+X 0 1 X^3 1 X^2 0 1 X X^3+X^2+X X^2 X 1 X 1 1 X^2 0 1 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+X^2+X+1 1 1 X+1 X^3 X^3+X X^2 X^3+1 X^3+1 X^3+X^2 X+1 1 X X^2 1 X^2 X^3 X^3+1 X+1 X^2+X X^3+X+1 1 X^3+X 1 X^3+X^2+X 1 X^3+X X^2 X+1 1 X^3 X^2+X X^3+X^2+X 1 X+1 1 1 X^2 1 1 1 X^3 X X^2+X 0 1 1 X^3+X^2 1 X^3+X^2+X X^3+X X^3+X^2+X 1 X^2+X+1 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 1 X^3+1 X^3+X 1 X^3+X^2+X+1 0 X^3 X^2+1 X^3+X^2+X+1 X^3 X^2+1 1 X^3+X^2+X X^3+X^2 X^3+X^2+X+1 X^2+X X X^2+X+1 X^3+X X^3+X^2+1 0 X+1 X^3+X^2+1 X^2 X 1 X X^3+X^2+X+1 X^3+X^2+1 1 X^3+X^2+X+1 X^3+X X^2+X X^2+1 X^3+X^2 X^2 X^3+X^2+X X^2 X^2 X^3+X^2+X+1 1 X^2+X 1 0 X^3 X+1 X^3+X^2+X X^2+X+1 X^3+X^2 X^3+X+1 X^3+X X^3+X X^2 X 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 X^3+X^2+X+1 X^2+1 X^3+X^2 X^3+1 X^2+1 X^3+X^2+1 X^3+X^2+1 X^2+X X^3+1 X^3+X+1 1 X^3+X^2 X^2+X 1 X^2+X+1 X^3+1 X^3+X^2 X^3+X^2+X X^3+X^2+X+1 X^2 X^3+X^2 X^2 X+1 X X^3+X^2+X+1 X X^3+X^2+X+1 1 X X+1 X^3+X^2+1 X^3+X^2 X X^3 X^2+1 X^2+X X^3+X^2+1 X^2+1 X+1 X^2+1 X+1 X^3+X+1 X+1 X^2+X+1 1 X^3 X X+1 0 X^3+X X^3+X^2+1 1 X^3+1 X^3 0 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+388x^75+1788x^76+2830x^77+4849x^78+5456x^79+7069x^80+7004x^81+7969x^82+6520x^83+6997x^84+5218x^85+4230x^86+2366x^87+1564x^88+588x^89+396x^90+164x^91+61x^92+56x^93+13x^94+2x^95+7x^98 The gray image is a linear code over GF(2) with n=656, k=16 and d=300. This code was found by Heurico 1.16 in 47.5 seconds.