The generator matrix

 1  0  0  1  1  1 X^3+X X^3+X  1  1 X^2+X  1  1 X^2  1  1  0 X^3+X^2 X^3+X  1 X^3 X^2  1  1 X^3  1
 0  1  0  0 X^3+X^2+1 X+1  1  1 X^2+X X^2+1 X^3  X X^3+X^2+1  1 X^2+X+1 X^3+X^2+X+1  1  1  X X^3+X  1  1 X^2 X^2+X+1  1  1
 0  0  1 X+1 X+1  0  1 X^2+X X^3  1  1  1 X^2+X X^3+X^2+X+1 X^3+1 X^3+X^2+X X^2+X X^3+1  1 X^3+X X+1 X^3+X^2+1 X^2  0  X X^3+X^2+1
 0  0  0 X^2 X^3+X^2 X^3 X^2 X^3  0 X^3+X^2  0 X^3 X^2  0  0 X^3+X^2 X^3 X^3 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^3 X^3+X^2  0 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+354x^22+968x^23+1991x^24+3176x^25+3405x^26+3292x^27+1973x^28+828x^29+292x^30+44x^31+40x^32+12x^33+5x^34+3x^36

The gray image is a linear code over GF(2) with n=208, k=14 and d=88.
This code was found by Heurico 1.16 in 132 seconds.