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 1 1 1 1 1 1 1 1 1 1 X^3 1 1 1 1 1 1 1 1 0 X X^3+X^2 0 X X X 0 0 X X^3+X^2 X^2+X 0 X^2+X X^3+X^2 X^3+X 0 X^2+X X^3+X X^3+X^2 X^3 X^3+X^2+X X^2 X^3+X 0 X^2+X X^3+X X^3+X^2 X^2+X 0 X^3+X^2 X^3+X X^2+X 0 X^3+X X^3+X^2 X^3+X^2+X X^3 X^2 X 0 X^2+X X^3+X^2 X^3+X X^3+X^2+X 0 X^2 X X^2+X X^3 X^3+X X^2 X^3+X^2+X X^3 X^3+X^2 X 0 X^3 0 X^2+X X^3+X^2+X X^2+X X^3 X^3+X^2+X X^3+X^2 X^3+X^2 X^2 X^2 X^3+X X^3+X X X X^3 0 0 X^3 X^3 X^2+X X^2+X X^3+X^2+X X^3+X^2+X X X^2+X X X X^3+X X^2+X X^2+X X 0 0 X^3 0 0 0 X^3 0 0 0 0 X^3 0 0 X^3 0 0 X^3 X^3 0 X^3 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 X^3 0 0 X^3 X^3 X^3 X^3 0 X^3 X^3 X^3 0 0 0 0 0 0 X^3 X^3 0 0 0 0 0 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 0 X^3 0 0 0 X^3 0 0 0 0 0 X^3 0 X^3 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 X^3 0 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 0 0 X^3 0 X^3 X^3 0 0 0 0 0 0 0 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 0 X^3 0 0 0 0 X^3 0 X^3 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 X^3 0 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 0 0 X^3 X^3 X^3 0 X^3 0 0 0 0 X^3 X^3 0 X^3 0 X^3 0 X^3 0 0 X^3 X^3 0 0 X^3 0 0 0 0 X^3 X^3 0 0 0 0 0 0 0 X^3 0 X^3 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 0 X^3 0 X^3 0 0 X^3 X^3 0 X^3 0 X^3 X^3 0 0 0 X^3 0 X^3 0 0 X^3 0 0 X^3 0 X^3 0 X^3 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 X^3 0 0 X^3 0 X^3 0 X^3 0 0 X^3 0 X^3 0 X^3 X^3 0 X^3 0 0 X^3 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+65x^76+32x^77+288x^78+256x^79+252x^80+448x^81+128x^82+256x^83+62x^84+32x^85+224x^86+2x^88+1x^92+1x^144 The gray image is a linear code over GF(2) with n=648, k=11 and d=304. This code was found by Heurico 1.16 in 0.672 seconds.