The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X X X X X 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 X 0 X X 0 0 X 0
0 X 0 0 0 X X X 0 0 0 X 0 X X X 0 0 X X 0 X X 0 X X X X 0 0 0 0 0 X 0 X X X 0 0 0 X X X X X X X X
0 0 X 0 X X X 0 0 0 X X X X 0 0 0 X X 0 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 X 0 0
0 0 0 X X 0 X X 0 X X 0 0 X X 0 X X 0 0 0 X X 0 0 X X 0 0 X X X X 0 0 X X 0 0 X X 0 0 X X X X 0 0
generates a code of length 49 over Z2[X]/(X^2) who´s minimum homogenous weight is 49.
Homogenous weight enumerator: w(x)=1x^0+16x^49+6x^50+6x^52+1x^54+1x^56+1x^62
The gray image is a linear code over GF(2) with n=98, k=5 and d=49.
As d=49 is an upper bound for linear (98,5,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 5.
This code was found by Heurico 1.16 in 0.0229 seconds.