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 X 1 1 1 1 1 1 1 1 1 1 1 X 1 X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X^3 1 1 1 1 1 1 1 0 1 1 X X 1 X X^2 X 1 X X 1 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^3+X X^3 X^3+X X^3 X^3+X X^2+X 0 X^3+X X^2 X X^3 X^2+X X^3+X^2 X^2+X X 0 0 X X X^2 X X^3 X^3+X^2+X X^3+X^2 X^2+X X^3 0 X^3+X X^3+X^2+X X^3 X^3+X^2+X X^3 X^2+X X^2+X X^2 X^3+X X^3 X^3+X X^3+X^2 X^2 X^3+X X^3+X^2 X X^2+X X X^3 X^3+X^2 X X^2 X^3+X^2+X X X^3+X X^3+X^2+X X^3+X^2+X X^3+X^2+X X^3+X^2 X^2+X X X^2+X 0 X X^3 X^3+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^3 X^2 0 0 0 X^3+X^2 X^3+X^2 0 X^2 X^2 0 X^3 X^3 X^2 X^2 X^3 X^2 X^3 X^3+X^2 0 X^3+X^2 0 X^3 0 0 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3 0 X^3 0 X^3+X^2 X^2 0 X^3+X^2 X^2 0 X^2 X^2 X^2 X^2 X^3 X^2 X^3 X^3 X^2 X^3+X^2 X^2 X^3 X^3+X^2 X^3 0 X^3 X^3+X^2 X^2 0 X^3+X^2 0 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 0 X^3+X^2 X^3+X^2 X^3 0 X^3+X^2 X^2 X^3+X^2 X^3+X^2 0 X^3 X^3 0 X^3+X^2 X^2 X^3 0 X^2 X^2 X^3 X^3 X^3+X^2 0 X^3+X^2 X^3+X^2 X^3+X^2 0 X^3 X^3+X^2 X^3 X^3+X^2 0 X^3 X^3+X^2 X^3+X^2 X^3 0 X^3+X^2 X^2 X^3 X^3+X^2 X^3 X^3+X^2 X^3 X^3+X^2 0 X^3 X^2 X^3 X^2 X^3+X^2 0 X^3 0 X^2 X^3 X^3 X^2 X^3 X^3 X^3+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 0 X^3 X^3 0 X^3 X^3 X^3 X^3 0 X^3 X^3 0 0 0 X^3 X^3 X^3 0 X^3 X^3 X^3 X^3 0 X^3 X^3 X^3 0 X^3 0 X^3 0 X^3 0 X^3 X^3 0 0 X^3 0 0 0 X^3 X^3 0 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 82 over Z2[X]/(X^4) who´s minimum homogenous weight is 76. Homogenous weight enumerator: w(x)=1x^0+230x^76+28x^77+252x^78+144x^79+493x^80+588x^81+746x^82+608x^83+437x^84+148x^85+154x^86+16x^87+132x^88+4x^89+62x^90+31x^92+2x^94+14x^96+5x^100+1x^140 The gray image is a linear code over GF(2) with n=656, k=12 and d=304. This code was found by Heurico 1.16 in 5 seconds.