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 X X 1 1 1 1 0 X 0 X^3+X^2+X X^3 X^2+X X^3 X^3+X 0 X^2+X X^3 X^3+X X^3 X^3+X^2+X 0 X 0 X^3+X^2+X X^3 X^3+X 0 X^2+X X^3 X 0 X^3+X^2+X X^3 X^3+X X^3 X^2+X X^3 X^3+X X^3+X^2 X^3+X X^2 X^3+X^2+X X^2 X^3+X^2+X X^3+X^2 X^3+X X X^3+X^2 X^3+X^2 X^2+X X^3+X^2 X^3+X X^2+X X^3+X^2 X^3+X^2 X^3+X X^2 X^3+X^2+X X^3+X^2 X^3+X^2+X X^2 X X^2 X^3+X X^3+X^2 X^3+X^2+X X^3+X^2+X X^3+X^2 X^2 X X^3 X X^3+X X^2+X X^3+X^2 X^3 X^3+X^2 X^2+X X^2 X^3+X^2+X X^2 X^3 X X^3+X^2+X 0 X^3+X^2 X^2 X X^3+X X^3+X X^2+X 0 0 X^3+X^2 X^2 X^3+X^2+X X^3+X^2+X X^2+X X^3+X X X^3+X^2+X X^2+X 0 0 X^3+X^2 0 0 X^3+X^2 X^2 X^2 0 0 0 0 X^2 X^3+X^2 X^3+X^2 X^2 X^3 X^3 X^3 X^3 X^3+X^2 X^2 X^2 X^3+X^2 X^3 X^3 X^3 X^3 X^3+X^2 X^2 X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^3+X^2 0 X^3 0 0 X^2 X^2 X^2 X^3+X^2 0 X^3 0 X^3 0 X^3+X^2 X^3+X^2 X^2 X^3 0 X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3 X^3 X^3 0 X^3+X^2 0 X^2 X^3+X^2 X^3+X^2 0 0 X^3 0 0 X^3+X^2 X^3+X^2 X^3 X^2 0 X^3 X^3 X^3 0 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^3+X^2 X^3+X^2 0 0 0 X^3+X^2 X^2 X^3+X^2 X^2 0 X^3 X^2 X^3+X^2 X^3 X^3+X^2 X^2 X^3 X^3 X^3 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^3+X^2 X^3 X^3 X^2 X^2 X^3 0 X^3+X^2 X^3 0 X^2 X^3+X^2 X^3+X^2 X^3 X^3 X^2 X^2 0 X^3 X^3 X^2 X^2 0 X^3+X^2 X^3 0 X^3+X^2 0 X^3+X^2 X^3+X^2 X^3 0 X^2 0 X^3+X^2 0 X^2 X^3 X^2 X^2 0 X^3+X^2 0 X^2 0 X^3+X^2 X^3 X^2 X^2 X^3+X^2 0 X^3 X^3 0 0 0 X^2 X^2 X^3 X^3 X^3+X^2 0 X^2 X^3+X^2 X^2 X^3 X^3+X^2 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+168x^92+48x^93+120x^94+208x^95+976x^96+208x^97+96x^98+48x^99+163x^100+8x^102+3x^104+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 1.23 seconds.