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
0 X 0 0 0 0 0 0 0 X X X X X X X 0 0 0 0 0 0 0 X X 0 X X X X X X 0 0 0 0 X X 0 0 X X 0 0 X X X X
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 0 0 0 0 0 0 0 X X 0 0 X X 0 X X X X 0 0
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 0 X X 0 0 X X X X 0 0 0 X X 0
0 0 0 0 X X 0 X X 0 X X X 0 0 X 0 X X 0 0 X X 0 X 0 X 0 0 X X 0 0 X X 0 0 0 0 X X 0 X 0 X 0 X X
generates a code of length 48 over Z2[X]/(X^2) who´s minimum homogenous weight is 48.
Homogenous weight enumerator: w(x)=1x^0+62x^48+1x^96
The gray image is a linear code over GF(2) with n=96, k=6 and d=48.
As d=48 is an upper bound for linear (96,6,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 6.
This code was found by Heurico 1.16 in 0.0206 seconds.