The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  1  1  1  1 X^2 X^2  X X^2
 0 X^3+X^2  0 X^3+X^2  0 X^3+X^2 X^3 X^2  0 X^3+X^2  0  0 X^3+X^2 X^2 X^3+X^2 X^3 X^2 X^3 X^3 X^2 X^3 X^3 X^3+X^2 X^3+X^2 X^3 X^3
 0  0 X^3  0  0  0 X^3  0  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0  0  0
 0  0  0 X^3  0  0  0 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0  0  0 X^3 X^3 X^3
 0  0  0  0 X^3  0 X^3  0  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3
 0  0  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3  0  0 X^3 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+48x^22+16x^23+165x^24+48x^25+498x^26+48x^27+138x^28+16x^29+20x^30+13x^32+10x^34+2x^36+1x^40

The gray image is a linear code over GF(2) with n=208, k=10 and d=88.
This code was found by Heurico 1.16 in 0.047 seconds.