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 X^2 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 X 1 1 1 1 1 1 1 1 1 X 1 1 X^2 1 1 1 X^3+X^2 1 X 1 1 X 1 0 X^3+X^2 1 1 0 1 1 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^2 X^3+X X^2+X X^3+X^2 X^2+X X^2 X X X^3+X^2 0 X X^3 X^2+X 0 X^3+X^2+X X^3+X^2+X X^2 X X^3 X^2+X X^3+X^2 X^3+X^2+X X^2 X^3+X^2+X X^3+X^2 X^3+X X^3+X^2 X X^3+X X X^3+X^2 X^2 X^2 X^3 X X 0 X^3 0 0 X X^2+X X^2 X^3+X^2+X 0 X^3 X^2+X X^2 X^3+X^2 X^2+X X^3+X X^3 X^3 X^3+X^2 X^3+X^2+X 0 X X^3+X 0 X X X^3+X^2 X^3 0 0 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 X^3+X^2+X X^3 X^2 X^3+X^2+X X^2+X X^2 X^3 0 X X X^2+X X^3+X X^3+X^2 X^3 X^3+X^2 X^3+X^2+X X^2 X^3 X^2+X X^3 X X^3+X^2 X^3 X^3+X X X^3+X X^3+X^2 X^2 X^2+X X^3+X X^3+X^2+X X^2 X^3 X^3+X^2 X^3+X X^3+X^2+X X^3+X^2+X X^3+X^2 X 0 X^2 X^3+X^2+X X^2 X X^2 X^2+X X X^3 X 0 X X X^3+X X^3+X 0 X^3+X^2 X^2+X X X^3 X^2+X X^3 X X^3 0 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 0 0 0 X^3 X^3 0 0 X^3 0 X^3 X^3 X^3 0 X^3 X^3 0 X^3 X^3 X^3 X^3 0 X^3 0 0 X^3 0 0 X^3 X^3 0 X^3 0 0 X^3 0 0 0 X^3 0 X^3 0 X^3 0 0 X^3 X^3 0 X^3 X^3 0 X^3 0 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 X^3 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 0 0 X^3 0 0 X^3 0 0 0 X^3 X^3 0 X^3 X^3 X^3 X^3 0 0 0 X^3 X^3 0 0 0 X^3 0 X^3 X^3 0 X^3 0 0 X^3 X^3 0 X^3 0 X^3 0 0 X^3 0 X^3 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 X^3 X^3 0 X^3 X^3 0 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+51x^76+218x^77+228x^78+350x^79+402x^80+630x^81+472x^82+612x^83+393x^84+258x^85+175x^86+178x^87+25x^88+30x^89+27x^90+12x^91+8x^92+16x^93+8x^94+1x^98+1x^142 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 0.969 seconds.