The generator matrix

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

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+234x^24+128x^25+320x^26+128x^27+200x^28+12x^32+1x^48

The gray image is a linear code over GF(2) with n=208, k=10 and d=96.
This code was found by Heurico 1.16 in 0.14 seconds.