The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 1 1 1 1 1 1 X X^2 1 0 1 X 1 1 1 X 1 0 X X 1 X X 0 1 X 1 X X^3+X^2 0 X 0 X 0 X^3 X^3+X X X^2 X^2+X X^2 X^3+X^2+X X^2 X^3+X^2 X^3+X^2+X X^3+X^2+X 0 X^3+X^2 X X^3+X^2+X X 0 X^3 X 0 X^2+X X^2+X X^3+X^2+X X^3+X^2 X^2 X^3+X^2 X^3+X^2+X 0 X^3+X X^3 X X^2 X^3+X X^3+X^2+X X^3+X^2+X X X^3+X^2 X^2 X^3+X 0 X^2 X^3 X^3+X X^2 X X^3 X^2 X X^3 0 X^3+X^2+X X^2+X X X^3+X^2 0 X^2 X^2 X X X^2 X^3+X^2+X X^3+X^2+X X^3+X^2+X X^3+X X^3 X X^3 X^3+X^2 X^2 X^3+X X^3+X^2+X X^3 X X^3+X^2+X X^2+X X^2+X X^3+X X 0 0 X X X^3+X^2 X^3+X^2+X X^2+X X^2 X^2 X^3+X^2+X X 0 X^3 X^3+X^2+X X^3+X X^2 0 X^3+X X X^2 X^3+X^2+X X X^2 X^2 X^2+X X^3+X^2+X X^3 X^3+X X^3+X^2 X^2+X 0 X^3 X^3+X X^3 0 X^3+X X^3+X X^3+X^2 X^3+X^2+X X X^3 X^3 X X^3+X^2+X 0 X^3+X^2 X^2+X 0 X^3+X^2+X X^2 X^2 X^3+X^2+X X^3+X^2 X^2 X^2+X X^2 X^3+X^2 X^3+X X^3 X^3+X X^3+X^2+X X X^2+X X^3 X^2 X^3+X^2 0 X X^3+X^2 X^3 X^3+X^2+X X X^3+X X^3+X^2+X X^2 X^2 X 0 X^3+X^2+X X^3+X^2 X X^3+X^2+X X^2+X 0 0 0 X^3 0 0 X^3 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 X^3 0 0 0 X^3 X^3 X^3 0 X^3 X^3 0 X^3 0 X^3 X^3 X^3 X^3 0 0 0 0 0 0 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 0 0 0 0 0 X^3 X^3 0 0 0 0 X^3 X^3 X^3 X^3 0 0 0 0 X^3 X^3 0 0 0 0 0 X^3 0 X^3 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 X^3 0 X^3 X^3 X^3 0 0 X^3 X^3 0 X^3 0 0 X^3 X^3 0 0 X^3 0 0 0 X^3 X^3 X^3 0 0 X^3 X^3 X^3 0 0 0 0 X^3 X^3 X^3 X^3 X^3 0 0 0 0 X^3 0 X^3 0 X^3 0 0 0 0 X^3 0 X^3 0 X^3 X^3 0 X^3 0 X^3 X^3 X^3 0 X^3 X^3 X^3 0 X^3 X^3 generates a code of length 83 over Z2[X]/(X^4) who´s minimum homogenous weight is 78. Homogenous weight enumerator: w(x)=1x^0+447x^78+40x^79+512x^80+256x^81+615x^82+432x^83+625x^84+256x^85+501x^86+40x^87+238x^88+85x^90+19x^92+16x^94+12x^96+1x^136 The gray image is a linear code over GF(2) with n=664, k=12 and d=312. This code was found by Heurico 1.16 in 15.9 seconds.