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 X X X X X X X X X 0 0 X 0 X X 0 0 0 0 0 0 0 0 0
0 X 0 0 0 0 0 0 0 X X X X X X X 0 0 0 0 0 0 0 0 X X X X 0 0 X X 0 X 0 X X X 0 X X X X X X 0 X X 0 X X 0
0 0 X 0 0 0 X X X X X 0 X X 0 0 0 0 0 0 X X X X X X X X X X X X X X X X 0 X X 0 X 0 0 0 0 X 0 X X 0 X X
0 0 0 X 0 X X X 0 0 0 0 X X X X 0 0 X X X X 0 0 0 0 X X X X 0 0 0 X 0 X X X 0 0 0 X 0 0 X X 0 X 0 X 0 X
0 0 0 0 X X 0 X X 0 X X X 0 0 X 0 X X 0 0 X X 0 0 X X 0 0 X 0 X X X 0 0 0 0 X X X X 0 X 0 0 0 X 0 X 0 X
generates a code of length 52 over Z2[X]/(X^2) who´s minimum homogenous weight is 52.
Homogenous weight enumerator: w(x)=1x^0+56x^52+4x^56+3x^64
The gray image is a linear code over GF(2) with n=104, k=6 and d=52.
As d=52 is an upper bound for linear (104,6,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 6.
This code was found by Heurico 1.16 in 6.67 seconds.