The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 0 X 0 X X 0 X X^2 X^2 X X X 0 X 0 X^2+X 0 X^2+X 0 X X^2 X^2+X X^2 X X^2 X^2+X X^2 X X^2+X X X^2+X X 0 X^2+X X X X 0 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 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 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 0 generates a code of length 29 over Z2[X]/(X^3) who´s minimum homogenous weight is 28. Homogenous weight enumerator: w(x)=1x^0+92x^28+31x^32+4x^36 The gray image is a linear code over GF(2) with n=116, k=7 and d=56. As d=57 is an upper bound for linear (116,7,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 7. This code was found by Heurico 1.16 in 0.0149 seconds.