The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3+X^2  1  1 X^3+X  1  1 X^3  1  1 X^3+X^2+X  1  1  1  1 X^2  X  1  1
 0  1 X+1 X^2+X X^2+1  1 X^3+X^2 X^3+X^2+X+1  1 X^3+X X^3+1  1 X^3 X^3+X+1  1 X^3+X^2+X X^3+X^2+1  1 X^2  X X^2+X+1  1  1  1  0 X^2+X

generates a code of length 26 over Z2[X]/(X^4) who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+24x^25+204x^26+24x^27+1x^32+2x^36

The gray image is a linear code over GF(2) with n=208, k=8 and d=100.
As d=102 is an upper bound for linear (208,8,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 8.
This code was found by Heurico 1.16 in 3.62e-008 seconds.