The generator matrix

 1  0  1  1  1 X^3+X^2+X  1  1  0  1  1 X^3+X^2+X X^3  1  1 X^2  1  1  1  1  1  1  1 X^2+X  1  1
 0  1 X+1 X^3+X^2+X X^2+1  1 X^3+X+1  0  1 X^3+1 X^3+X^2+X  1  1 X^3+X^2 X^3+X^2+1  1 X^3 X^3+X^2+X+1  0 X^2+X X^3+X^2+1 X^2+X+1 X^2+X+1  1 X^3+X^2 X^3
 0  0 X^2  0  0 X^3  0 X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3 X^3+X^2  0 X^2 X^3 X^3 X^3+X^2  0 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3 X^2
 0  0  0 X^3+X^2 X^3 X^2 X^2 X^3+X^2 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^3+X^2 X^2  0 X^3+X^2 X^3  0  0 X^3 X^2 X^3+X^2 X^3+X^2 X^2  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+52x^22+258x^23+406x^24+1036x^25+635x^26+1028x^27+380x^28+220x^29+47x^30+6x^31+13x^32+8x^33+1x^34+4x^35+1x^38

The gray image is a linear code over GF(2) with n=208, k=12 and d=88.
This code was found by Heurico 1.16 in 0.078 seconds.