The generator matrix

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

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+176x^22+236x^23+532x^24+664x^25+936x^26+656x^27+492x^28+232x^29+104x^30+4x^31+59x^32+4x^36

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 0.11 seconds.