The generator matrix

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

generates a code of length 26 over Z2[X]/(X^4) who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+64x^23+66x^24+96x^25+640x^26+32x^27+56x^28+32x^29+32x^31+4x^32+1x^48

The gray image is a linear code over GF(2) with n=208, k=10 and d=92.
This code was found by Heurico 1.16 in 0.109 seconds.