The generator matrix

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

generates a code of length 26 over Z2[X]/(X^4) who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+188x^23+209x^24+492x^25+384x^26+432x^27+152x^28+112x^29+52x^31+21x^32+4x^33+1x^40

The gray image is a linear code over GF(2) with n=208, k=11 and d=92.
This code was found by Heurico 1.16 in 20.5 seconds.