The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  X  1  1
 0 X^3  0  0  0  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3  0 X^3 X^3  0  0 X^3 X^3  0
 0  0 X^3  0  0  0 X^3 X^3  0 X^3  0  0 X^3  0 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3
 0  0  0 X^3  0  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3
 0  0  0  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0
 0  0  0  0  0 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0  0 X^3 X^3

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+11x^22+32x^24+429x^26+28x^28+5x^30+2x^32+3x^34+1x^48

The gray image is a linear code over GF(2) with n=208, k=9 and d=88.
This code was found by Heurico 1.16 in 1.05e-007 seconds.