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 X X 1 X 1 1 X 1 1 X 1 1 1 1 1 X 1 1 1 1 X 1 1 1 X X 1 X 1 X 1 1 1 1 1 X 1 1 X^2 1 1 X X 1 X X^2 1 1 1 X X X 1 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 0 0 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 0 0 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 0 0 0 0 0 X^2 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 0 X^2 0 0 X^2 0 0 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 0 0 X^2 0 0 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 0 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 0 0 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 0 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 0 0 0 X^2 X^2 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 0 0 0 0 X^2 0 0 generates a code of length 96 over Z2[X]/(X^3) who´s minimum homogenous weight is 84. Homogenous weight enumerator: w(x)=1x^0+148x^84+10x^86+224x^88+86x^90+286x^92+680x^94+1346x^96+668x^98+230x^100+74x^102+157x^104+14x^106+76x^108+4x^110+53x^112+26x^116+10x^120+2x^124+1x^152 The gray image is a linear code over GF(2) with n=384, k=12 and d=168. This code was found by Heurico 1.16 in 9.02 seconds.