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 X X
0 X 0 X^2+X 0 X^2+X 0 X 0 X^2+X X^2 X^2+X 0 X^2+X X^2 X^2+X 0 X^2+X X^2 X X^2 X X^2 X 0 X^2
0 0 X^2 0 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0
0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 0 0 X^2 0 X^2 X^2
0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2
generates a code of length 26 over Z2[X]/(X^3) who´s minimum homogenous weight is 24.
Homogenous weight enumerator: w(x)=1x^0+66x^24+128x^26+56x^28+4x^32+1x^48
The gray image is a linear code over GF(2) with n=104, k=8 and d=48.
As d=49 is an upper bound for linear (104,8,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 8.
This code was found by Heurico 1.16 in 0.00736 seconds.