The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3+X^2  1  1 X^3+X  1  1  0  1  1 X^2+X  1  1  X  1  1  0  0  1
 0  1 X+1 X^2+X X^2+1  1 X^3+X^2 X^3+X^2+X+1  1 X^3+X X^3+1  1  0 X+1  1 X^2+X X^2+1  1  0 X^3+X  0 X^3+1 X^2+1  X  X X^3
 0  0 X^3  0  0 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3  0  0 X^3  0 X^3
 0  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0  0  0  0  0 X^3  0 X^3 X^3 X^3  0
 0  0  0  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3  0  0  0 X^3 X^3  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+24x^22+144x^23+254x^24+368x^25+466x^26+384x^27+256x^28+112x^29+19x^30+16x^31+1x^32+2x^34+1x^46

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 0.031 seconds.