The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  0  1  X X^3+X^2  1 X^2  1  1 X^2
 0  X X^3+X^2 X^2+X  0 X^2+X X^3+X^2 X^3+X X^3+X^2 X^2+X  0 X^3 X^3+X X^3+X X^2+X X^3+X X^3+X^2+X  X  0 X^3+X  X X^2+X X^3+X^2 X^3+X X^3+X  0
 0  0 X^3  0  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0  0  0  0 X^3 X^3
 0  0  0 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0 X^3  0  0 X^3 X^3  0
 0  0  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3
 0  0  0  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3  0 X^3 X^3  0  0 X^3  0 X^3  0  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+121x^22+401x^24+256x^25+532x^26+256x^27+344x^28+110x^30+21x^32+4x^34+1x^38+1x^40

The gray image is a linear code over GF(2) with n=208, k=11 and d=88.
This code was found by Heurico 1.16 in 131 seconds.