The generator matrix 1 0 1 1 1 X^2+X 1 X^3+X^2 1 1 1 X^3+X 1 1 X^3 1 X^3+X^2+X 1 1 1 X^2 1 1 X 1 1 0 1 X^2+X 1 1 0 1 1 X^2+X 1 1 X X^2 1 1 1 1 1 X^2 X 1 X X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X^3+X^2 1 1 X^3+X X^2 1 1 1 X 1 1 X^3+X^2 0 1 X+1 X^2+X X^2+1 1 X^3+1 1 X^3+X^2 X+1 X^3+X 1 X^3+X^2+X+1 X^3 1 X^3+X^2+X 1 X^3+X^2+1 X^2+X+1 X^2 1 X 1 1 0 X+1 1 X^2+X 1 X^3+X^2+X+1 X^3+X^2+1 1 0 X 1 X^3+X+1 1 1 1 X^2 X^2+X X^3+X^2+X+1 X^2 X^2+1 1 X X 1 X X^3+1 X^2+1 X^2+X+1 1 X^3+X^2+X+1 X^2+1 X^3+1 X^3+X^2+X+1 X^2+X+1 1 X^3+X+1 X^2+1 X^2+X+1 X^2+1 X^3+X+1 X^3+X^2+X+1 X^2+1 X^3+1 X^3+X^2+X+1 0 1 X^3+1 X^2+X 1 X X^2+X X^3+X^2 1 1 X X^3+X^2 1 0 0 X^2 0 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 X^2 X^3+X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2 0 X^3 0 0 0 X^3 X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 0 X^3 0 X^3+X^2 0 0 X^3 X^3 X^3+X^2 X^3 X^2 0 0 X^3+X^2 X^2 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^3+X^2 0 X^2 0 X^3 0 X^3 X^3 X^2 0 0 X^3+X^2 X^3 X^3 0 X^3+X^2 X^2 0 0 0 0 0 X^3 0 X^3 X^3 0 X^3 X^3 0 X^3 0 0 X^3 X^3 0 X^3 X^3 X^3 X^3 0 0 0 0 X^3 X^3 X^3 0 0 0 0 0 0 X^3 0 X^3 X^3 0 X^3 X^3 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 X^3 0 X^3 0 0 0 0 0 0 0 X^3 0 0 0 X^3 X^3 0 0 0 0 X^3 0 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 0 0 X^3 0 X^3 0 X^3 0 0 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 0 0 0 0 0 0 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 X^3 0 0 0 0 0 0 X^3 X^3 X^3 0 X^3 0 X^3 0 X^3 0 0 generates a code of length 81 over Z2[X]/(X^4) who´s minimum homogenous weight is 76. Homogenous weight enumerator: w(x)=1x^0+113x^76+240x^77+630x^78+384x^79+617x^80+408x^81+544x^82+224x^83+490x^84+208x^85+76x^86+64x^87+65x^88+8x^89+10x^90+8x^92+2x^94+2x^98+1x^112+1x^116 The gray image is a linear code over GF(2) with n=648, k=12 and d=304. This code was found by Heurico 1.16 in 0.859 seconds.