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^2 X X X X^2 1 1 1 1 1 1 1 1 X X X X X X X X 1 1 X^2 X^2 0 0 0 X^2
0 X 0 X^2+X X^2 X^2+X X^2 X 0 X^2+X 0 X^2+X X^2 X X^2 X X^2+X X X^2+X X X X 0 X^2 X X 0 X^2 0 X^2 X^2+X X X^2+X X 0 X^2 X^2+X X^2+X X X 0 X^2 0 X^2 0 X^2 X^2 0 X X
0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0
generates a code of length 50 over Z2[X]/(X^3) who´s minimum homogenous weight is 50.
Homogenous weight enumerator: w(x)=1x^0+52x^50+3x^52+4x^54+3x^56+1x^60
The gray image is a linear code over GF(2) with n=200, k=6 and d=100.
As d=100 is an upper bound for linear (200,6,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 6.
This code was found by Heurico 1.16 in 0.0563 seconds.