The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  X X^2  1  1  1  1  X  1  1
 0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^2 X^3  0 X^3+X^2  0 X^3+X^2 X^3+X^2 X^2  0 X^3 X^3+X^2 X^3+X^2 X^3  0 X^3 X^3+X^2 X^3+X^2 X^3+X^2  0
 0  0 X^3  0  0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0  0 X^3  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  0  0 X^3 X^3  0 X^3  0  0  0
 0  0  0  0 X^3  0  0  0  0 X^3 X^3 X^3  0  0  0 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0
 0  0  0  0  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3  0  0 X^3  0  0 X^3 X^3  0
 0  0  0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0

generates a code of length 26 over Z2[X]/(X^4) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+16x^20+48x^21+34x^22+64x^23+50x^24+528x^25+578x^26+528x^27+43x^28+64x^29+22x^30+48x^31+13x^32+6x^34+4x^36+1x^44

The gray image is a linear code over GF(2) with n=208, k=11 and d=80.
This code was found by Heurico 1.16 in 0.046 seconds.