The generator matrix

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

generates a code of length 25 over Z2[X]/(X^4) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+126x^21+319x^22+444x^23+927x^24+586x^25+874x^26+352x^27+274x^28+130x^29+23x^30+20x^31+14x^32+6x^33

The gray image is a linear code over GF(2) with n=200, k=12 and d=84.
This code was found by Heurico 1.16 in 0.11 seconds.