The generator matrix

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

generates a code of length 25 over Z2[X]/(X^4) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+255x^22+48x^23+608x^24+288x^25+558x^26+48x^27+190x^28+51x^30+1x^40

The gray image is a linear code over GF(2) with n=200, k=11 and d=88.
This code was found by Heurico 1.16 in 1.55 seconds.