The generator matrix

 1  0  0  1  1  1 X^3+X X^2+X  1  1  1  1  0  1 X^3 X^3+X^2 X^2  1 X^3+X  1  X X^3+X^2+X X^3+X  1 X^3  1
 0  1  0 X^2 X^2+1  1  1 X^2+X X^3+1 X^2+1  0 X^3+X  1 X^2+X+1 X^3+X^2+X  1  1 X+1  1 X^3+X^2+X  1  1  1 X^3+X^2+1 X^2+X  0
 0  0  1 X^2+X+1 X+1 X^2 X^2+1  1 X^3+X X^2+1 X^3+1  0 X^2+X X^3+X^2  1 X+1 X^3+X^2+1 X^2+1 X^3+X+1 X^2+X+1 X^2+X X^2+X+1 X^2+1 X^3  1  0
 0  0  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3  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+97x^22+508x^23+1056x^24+1648x^25+1801x^26+1484x^27+910x^28+464x^29+149x^30+48x^31+17x^32+8x^33+1x^34

The gray image is a linear code over GF(2) with n=208, k=13 and d=88.
This code was found by Heurico 1.16 in 0.407 seconds.