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 X^3 1 1 X 1 1 1 1 1 1 1 X^3 X^2 1 X 1 X^3+X^2 1 0 X 1 1 X 1 X 1 X X^2 1 X^2 1 X^3 0 1 X X 1 0 X 0 X X^3 0 X^2+X X^3+X^2+X 0 X^3 X^3+X X X^3 X^3+X^2+X X^3 X^3+X^2+X X^2 X^3+X X^3+X^2 X^3+X X^2 X^3+X^2+X X^2 X^2+X X^3+X^2+X X^2 X^2+X X^2 X 0 X X^3 X^3+X^2 X^3+X^2+X X^3+X^2+X X^2 0 X X^3+X X^3 X^3+X^2 X X^3+X^2 X^3+X^2 X^3+X^2+X X^2+X X^2 X^2+X X^2 X^3+X X^3 X^3+X^2+X X^2 X^2 X^2+X X^3+X X^3+X^2+X X^3 X^3+X X X^3+X^2 X^3+X X^3 0 0 X X^3+X^2+X 0 X^2+X X X^2+X X X^3 X^3 X X^3+X^2+X 0 X^3+X X^3+X^2+X X^3+X^2 X^2 X X X^2+X 0 X X^3+X^2 X X 0 0 0 X X 0 X^3+X^2+X X^2+X X^3 X^2 X^3+X^2+X X^3+X^2+X X^2 X^3+X X^2 X^3+X^2 X X^2 X^2+X X^3+X X^3+X^2 X^2+X X^2+X X^2 0 0 X^2 X^3+X^2+X X^3+X^2+X 0 X X^2+X X^3 X^2+X X X^3+X^2 X^3+X^2 0 0 X X X^3 X^2+X X X^3+X X^3+X^2 X^2+X 0 X^3+X^2 X^3+X^2+X X^3 X^2+X X^3 X^3+X X X X^3+X X^3 X^2 X^3+X^2 X^3+X^2 0 X^3+X X^3+X^2 X^2+X X X^3+X^2 X X X^3+X^2 X^2 X^2+X X^2 X^3+X^2+X X^3+X^2 X^3+X^2+X X^2+X X^2 X 0 X^3+X^2+X X X^2 X^2+X X^3+X X X^3+X X^3+X^2 X^3 X^2 0 0 0 0 X^2 X^2 X^3+X^2 0 X^3+X^2 X^2 X^3 X^3+X^2 0 X^2 X^3+X^2 0 X^3 0 X^3 X^3+X^2 X^2 0 X^2 X^2 0 X^2 X^3+X^2 X^3+X^2 X^3 X^3 X^3+X^2 0 X^3 X^3+X^2 0 0 X^3 X^3+X^2 X^2 X^3+X^2 X^3 0 X^2 X^2 X^3 X^3 X^3 X^3+X^2 X^2 X^2 X^3+X^2 0 X^3 0 X^3 X^2 X^3 X^3+X^2 X^3 X^3 X^3+X^2 X^2 0 X^3+X^2 X^2 X^2 0 X^2 X^2 0 X^3 X^3+X^2 X^3+X^2 0 X^3 X^3+X^2 X^2 X^3+X^2 X^3 X^3+X^2 X^2 X^2 X^2 X^2 X^3 0 X^3 X^3 X^2 0 0 generates a code of length 90 over Z2[X]/(X^4) who´s minimum homogenous weight is 84. Homogenous weight enumerator: w(x)=1x^0+90x^84+224x^85+254x^86+408x^87+435x^88+520x^89+458x^90+522x^91+360x^92+240x^93+189x^94+144x^95+78x^96+84x^97+31x^98+30x^99+8x^100+4x^101+11x^102+4x^104+1x^146 The gray image is a linear code over GF(2) with n=720, k=12 and d=336. This code was found by Heurico 1.16 in 1.25 seconds.