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 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 0 1 X^3 1 0 X 0 X X^3 X^3 X^3+X X^3+X X^2 X^2+X X^2 X^2+X X^3+X^2 X^3+X^2+X X^3+X^2 X^3+X^2+X 0 X X^2 X^3+X X^3+X^2 X^3+X X^2+X X^2 0 X^3+X^2+X X^3+X X^2 0 0 X^2+X X^3+X^2+X X^3+X^2 X^2+X X^3 X^3+X X^2+X 0 X X^3+X^2 X^3+X^2+X X^3+X X^3+X^2 X^3 X^3+X 0 X^2+X X^3+X^2 X^2+X X^3+X^2 X^2 X^3+X^2+X X^3+X^2+X X^2 X^3 X^2+X X^3+X X^3+X^2 X^3 X X^3+X X^3 X^3 X^3+X X 0 X^3+X^2+X X^3+X^2 X^2+X 0 0 X^2+X X^2 X X^3+X^2+X X^2 X^2 X^3 X^2 X^3+X X^2+X X X^2 X X^3+X^2+X X^2 X^3+X^2+X X X^3 X 0 X^3+X^2+X X^3 X^3 X X^2 0 0 X X X^2 X^3+X^2+X X^2+X X^3+X^2 X^2 X^2+X X 0 0 X X^3+X^2+X X^3+X^2 0 X X X^3+X^2 0 X^2+X X^3+X^2 X^2+X X^3+X^2+X X^3+X X^3 X^3+X^2 X^2 X^3+X X^3+X^2+X 0 X^3+X^2 X^3 X^3+X X X^3+X^2 X^2+X X^3+X^2+X X^3 X^2+X X^2 X^3+X X^3+X^2 0 X^3 X^3+X X^3+X^2+X X X^3+X^2 X^3+X^2+X X^2 X^3+X^2+X X^3 X^3+X 0 X X X^3+X^2+X X^3+X^2+X X^2 X^3 X^3+X^2 X^3 X^2 X^3+X^2 0 X^2 X^2+X X^2+X X^3+X^2+X X^3+X^2+X 0 X^3 X^3+X^2 X^3+X X^2+X X X^3 X^3+X^2+X X 0 X^2 X^2+X X^2 X^3+X^2+X X^3+X X^2 X^2 X^3+X X^3+X^2 X^3+X^2+X X X^2+X X^3+X^2 X^3 0 0 0 X^3 X^3 X^3 0 X^3 0 X^3 X^3 X^3 X^3 0 0 0 X^3 0 0 0 0 X^3 X^3 X^3 0 X^3 X^3 X^3 0 X^3 0 0 X^3 X^3 0 0 0 X^3 X^3 0 0 0 0 X^3 X^3 0 X^3 X^3 0 0 0 X^3 X^3 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 0 0 0 X^3 X^3 0 0 0 X^3 X^3 X^3 0 X^3 X^3 0 X^3 0 X^3 X^3 X^3 X^3 0 0 X^3 0 X^3 0 X^3 0 0 0 0 0 0 generates a code of length 96 over Z2[X]/(X^4) who´s minimum homogenous weight is 92. Homogenous weight enumerator: w(x)=1x^0+116x^92+120x^93+149x^94+256x^95+761x^96+304x^97+130x^98+64x^99+113x^100+24x^101+9x^102+1x^188 The gray image is a linear code over GF(2) with n=768, k=11 and d=368. This code was found by Heurico 1.16 in 1.19 seconds.