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

generates a code of length 26 over Z2[X]/(X^4) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+42x^22+65x^24+64x^25+705x^26+64x^27+38x^28+20x^30+23x^32+1x^34+1x^48

The gray image is a linear code over GF(2) with n=208, k=10 and d=88.
This code was found by Heurico 1.16 in 0.016 seconds.