The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  X  1  1 X^2  1  1 X^2 X^2  X
 0 X^3+X^2  0 X^2  0  0 X^2 X^2 X^3 X^3 X^2 X^3+X^2  0 X^3 X^3 X^2 X^3+X^2 X^3+X^2 X^2 X^2 X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2
 0  0 X^3+X^2 X^2  0 X^3+X^2 X^3+X^2  0 X^3 X^2 X^2 X^2  0 X^2 X^2 X^2 X^3 X^3 X^3 X^3+X^2 X^2 X^3 X^2  0  0  0
 0  0  0 X^3  0  0 X^3  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0  0
 0  0  0  0 X^3  0  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3
 0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3  0  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 21.

Homogenous weight enumerator: w(x)=1x^0+28x^21+73x^22+118x^23+182x^24+370x^25+554x^26+376x^27+124x^28+104x^29+66x^30+14x^31+13x^32+10x^33+10x^34+4x^35+1x^38

The gray image is a linear code over GF(2) with n=208, k=11 and d=84.
This code was found by Heurico 1.16 in 0.047 seconds.