The generator matrix

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

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+20x^21+210x^22+656x^23+702x^24+976x^25+682x^26+620x^27+176x^28+24x^29+7x^30+4x^31+9x^32+4x^33+4x^34+1x^38

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 0.079 seconds.