The generator matrix

 1  0  1  1 X^2+X  1  1  1  X  1  1 X^3+X^2  1 X^3  1  1  0 X^2+X  1  1  1  1 X^3  1 X^3+X^2+X  1
 0  1  1 X^2+X  1 X^3+X+1 X^3+X^2+1 X^2  1  X X^3+X^2+X+1  1  X  1 X^3+1  0  X  1 X^3+X^2+X+1 X^2+X+1 X^3+X+1 X^2+X X^3 X^3+X^2+1  1  0
 0  0  X  0 X^3 X^2 X^3+X^2  X  X X^3+X X^2+X X^3+X^2+X X^2+X X^3+X X^3+X^2+X X^2+X X^2+X X^2+X X^3+X^2+X X^2 X^3 X^3+X^2  X X^2+X X^3+X  0
 0  0  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0  0  0 X^3  0 X^3  0  0 X^3 X^3  0 X^3 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+30x^22+272x^23+573x^24+786x^25+920x^26+732x^27+418x^28+224x^29+94x^30+20x^31+8x^32+14x^33+4x^34

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 0.062 seconds.