The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3+X^2  1  1 X^3+X  1  1  1  1  0 X^2+X  1  1  1 X^3+X X^3+X^2  1  1  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^2+X X+1 X^2+1  1  1 X^3+X^2 X^2+X X^3+1  1  1 X^3+X^2+X+1 X^3+X X^2+X
 0  0 X^3  0  0  0  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0
 0  0  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3  0 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0  0
 0  0  0  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3  0
 0  0  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0  0 X^3 X^3  0  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+1026x^24+1812x^26+1014x^28+110x^30+5x^32+4x^34+2x^36+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 12 seconds.