The generator matrix

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

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+184x^22+702x^23+778x^24+1018x^25+584x^26+474x^27+232x^28+102x^29+8x^30+8x^31+5x^32

The gray image is a linear code over GF(2) with n=200, k=12 and d=88.
This code was found by Heurico 1.16 in 0.39 seconds.