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 X 0 X 0 0 X X 0 0 X X 0 X X 0 0 0 X^2+X X^2+X 0 0 X^2+X X^2+X 0 X^2 X^2+X X 0 X^2 X X^2+X X^2 X X^2+X X^2 X X 0 X^2 X^2+X X^2 0 X X^2 X X^2 X^2+X X X^2 0 X^2+X X^2 0 X X X^2+X X^2 X^2 X X^2 X^2 X^2+X X X^2+X X^2 0 X^2+X 0 X^2+X X^2+X 0 X^2+X X^2+X X^2 X^2 0 0 X X^2+X X^2 X^2 X^2 X 0 X X^2+X X 0 X^2 X^2 0 0 0 X X 0 X^2+X X 0 X^2+X 0 X 0 0 X 0 X^2+X X^2+X 0 X^2+X 0 0 X X^2+X 0 0 X X X^2 X^2 X X X^2 0 X X^2 X^2+X X^2 X^2+X X^2+X 0 X^2+X X^2+X X^2 0 X X^2+X X^2 0 X^2+X X^2 X^2+X X^2 X^2+X X^2 X^2+X X^2 X 0 X X^2+X X^2 X 0 0 0 X^2+X X^2 X^2+X X^2 0 X X^2+X X^2 X^2+X 0 X^2+X X X^2 X 0 X^2 X^2+X X^2+X X^2 X X^2 0 X^2 X X^2 0 X^2 0 0 0 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 generates a code of length 92 over Z2[X]/(X^3) who´s minimum homogenous weight is 88. Homogenous weight enumerator: w(x)=1x^0+223x^88+576x^92+223x^96+1x^184 The gray image is a linear code over GF(2) with n=368, k=10 and d=176. This code was found by Heurico 1.16 in 18.5 seconds.