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

generates a code of length 26 over Z2[X]/(X^4) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+35x^24+8x^25+159x^26+22x^27+28x^28+1x^34+2x^35

The gray image is a linear code over GF(2) with n=208, k=8 and d=96.
This code was found by Heurico 1.16 in 3.62e-008 seconds.