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 1 1 1 1 1 0 1 1 1 X 1 1 1 1 1 0 1 X^3 1 1 1 1 0 1 X 1 1 1 X^3+X^2 X^2 1 X^3+X^2 X X^3 0 X 0 X^3+X^2+X X^2 X^2+X X^3+X^2 X 0 X^2+X X^3 X^2+X X^3+X X^2 X^2 X 0 X^2+X X^2 X X^3 X^3+X^2+X X^3 X^2+X X^3+X^2+X X^3+X^2 X^2 X X^2+X X^2 X^3+X X^3 X^2+X 0 X^3+X^2 X^3+X^2+X 0 X^2+X 0 X^3+X X^2 X^2+X X^3+X X^3+X X^3 0 X^3 0 X X X X^2+X X^3 X^3+X^2 X X^2+X X^3+X^2+X X^3+X X^2+X X^2 0 0 X^3+X X^3+X^2 X^2 X^2 X X^2+X X^3+X X^3+X X^2 0 X^3+X^2+X X^2 X 0 X^3 X X X^3 X X^2+X X 0 0 X^3+X^2 0 X^2 0 X^3 0 X^2 X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2 0 X^2 0 X^3+X^2 X^3 X^3 X^2 X^2 X^2 X^3 X^3 X^2 X^3 X^3 X^2 0 X^3+X^2 X^2 X^2 X^3 X^2 X^3 X^3 X^3 X^3 X^3+X^2 X^3 X^3+X^2 0 0 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3 0 X^3+X^2 X^2 X^2 X^3+X^2 X^2 X^3 X^3 X^3 X^3+X^2 X^3 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 0 X^3 X^2 X^2 X^3+X^2 X^2 X^2 X^2 X^3+X^2 0 X^2 0 X^3 X^2 0 0 0 0 X^3+X^2 0 X^3 X^3 X^2 X^2 X^2 X^2 0 0 X^2 X^3+X^2 X^2 X^3 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^3 0 X^2 0 X^2 0 X^2 X^2 X^3+X^2 X^3 0 X^3+X^2 X^3 X^3 X^3+X^2 X^3+X^2 X^3+X^2 0 X^3+X^2 X^3+X^2 0 X^3 X^3 X^2 X^3 X^3 X^2 0 0 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^3+X^2 0 0 X^2 X^2 0 X^2 0 X^3+X^2 X^2 0 X^2 X^2 X^3+X^2 X^3 0 X^3 X^3+X^2 X^3 X^3+X^2 X^3+X^2 0 0 X^3+X^2 X^3+X^2 X^2 X^2 0 0 0 0 X^3 X^3 X^3 X^3 0 0 0 X^3 0 X^3 X^3 X^3 0 0 X^3 0 0 X^3 0 0 X^3 X^3 X^3 X^3 X^3 0 0 X^3 X^3 0 0 0 X^3 X^3 X^3 0 0 0 X^3 0 X^3 0 X^3 0 X^3 0 0 0 X^3 0 X^3 X^3 0 X^3 0 X^3 X^3 0 0 0 X^3 0 0 X^3 0 X^3 X^3 X^3 0 0 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 generates a code of length 83 over Z2[X]/(X^4) who´s minimum homogenous weight is 77. Homogenous weight enumerator: w(x)=1x^0+170x^77+82x^78+330x^79+210x^80+466x^81+485x^82+726x^83+470x^84+428x^85+233x^86+218x^87+20x^88+138x^89+23x^90+68x^91+2x^92+14x^93+9x^94+2x^99+1x^144 The gray image is a linear code over GF(2) with n=664, k=12 and d=308. This code was found by Heurico 1.16 in 4.47 seconds.