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 X 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 X 1 1 1 X^3 1 0 1 1 1 X 1 1 1 1 1 1 0 X 1 X^3+X^2 1 1 X 1 X^2 X 1 1 1 X X 1 1 1 X^2 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^3+X^2 X X^3+X^2+X X X^2 X X^3 X^3 X^3 X^3+X X^2 X^3+X^2+X X^2+X X^3+X^2+X X^2 X^3+X 0 X^3+X^2 X^3 X^3+X X^3+X^2+X X^3+X 0 X^2+X X^2 X^2 X^3+X^2+X X^2 X^3 X^3+X^2+X X^2+X 0 X^3+X X X^2+X X^3 X^3+X X X^3 X^3 X^2 X^3+X^2+X X^2 X X^2 X^3+X X^2+X X^3 X^3+X X X X^3+X^2+X X^3 X^3 X^2 X^3 X^2 X^3+X^2 X^2 X^2+X X^3+X^2+X X^3+X^2+X X^3+X^2 X^3+X^2+X X^3+X^2 X^3+X X^3+X 0 X^2 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^3+X X X^2 X^3+X^2+X X^2 X^2 X X^3+X^2+X X^3+X^2 0 X^3+X^2+X X^2+X X^3+X 0 0 X^3 X^2+X X^3 X^3+X X^2+X X^3+X X^3+X^2 X^2 X^3+X^2 X^3+X X^2+X X^3+X X^3+X^2+X 0 X^3+X^2 0 X^3+X^2 X^3+X X^3+X X^2+X X^2+X X X^3+X^2 X^3 X X^3+X 0 X^2 X X^3 X^2 X^3+X^2+X X X^2+X X^2+X 0 X X^3 X X X^3+X^2 X^3+X X^3 X X^2 X^3 X^3 X^3 X^3+X X^3+X X^3 0 X X X^3 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 X^3 0 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 X^3 0 X^3 X^3 X^3 0 X^3 0 0 X^3 0 0 X^3 X^3 X^3 0 0 0 0 X^3 X^3 X^3 X^3 0 0 0 0 X^3 0 X^3 X^3 X^3 0 X^3 X^3 0 0 0 0 0 X^3 X^3 X^3 0 X^3 0 X^3 X^3 0 X^3 0 X^3 0 0 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 0 X^3 X^3 0 0 X^3 0 X^3 0 0 X^3 0 0 X^3 X^3 0 X^3 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 0 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 0 0 0 X^3 0 0 0 0 X^3 X^3 X^3 X^3 0 0 0 0 0 0 X^3 0 X^3 X^3 X^3 generates a code of length 87 over Z2[X]/(X^4) who´s minimum homogenous weight is 81. Homogenous weight enumerator: w(x)=1x^0+90x^81+200x^82+250x^83+355x^84+294x^85+724x^86+516x^87+660x^88+220x^89+293x^90+138x^91+107x^92+82x^93+54x^94+52x^95+24x^96+18x^97+9x^98+4x^99+4x^100+1x^144 The gray image is a linear code over GF(2) with n=696, k=12 and d=324. This code was found by Heurico 1.16 in 1.12 seconds.