The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^3  1  X  1  1
 0  X X^3+X^2 X^2+X  0 X^2+X X^3+X^2 X^3+X  0 X^2+X X^3+X^2 X^3+X  0 X^2+X X^3 X^3+X^2+X X^3+X^2 X^2 X^3+X X^3+X X^3+X^2 X^3 X^2+X X^2+X  0  0
 0  0 X^3  0  0  0 X^3 X^3 X^3  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
 0  0  0 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0  0  0 X^3  0 X^3  0 X^3 X^3 X^3  0
 0  0  0  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3  0  0  0  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+24x^22+32x^23+129x^24+272x^25+165x^26+240x^27+86x^28+16x^29+34x^30+16x^31+7x^32+1x^34+1x^48

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 0.016 seconds.