The generator matrix

 1  0  1  1  1 X^3+X^2+X  1  1 X^3+X^2  1  1 X^2+X  1  1 X^3+X  1  1 X^3  1  1  1 X^3  1 X^3 X^2
 0  1 X+1 X^2+X X^3+X^2+1  1 X^3+X^2 X^2+X+1  1 X^3+X^2+X  1  1 X+1 X^3+X  1 X^3 X^2+1  1 X^2 X^3+X^2+X X^2  X X^3+X^2+X+1  1  0
 0  0 X^2  0 X^3+X^2 X^2  0 X^2 X^3 X^2 X^2  0 X^3 X^3  0 X^2 X^3 X^2 X^2 X^2 X^3+X^2 X^2  0 X^3+X^2  0
 0  0  0 X^3  0  0 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0  0 X^3 X^3 X^3  0 X^3  0
 0  0  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0  0  0 X^3 X^3 X^3  0  0 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+98x^21+203x^22+656x^23+543x^24+1096x^25+639x^26+600x^27+119x^28+82x^29+21x^30+24x^31+8x^32+4x^33+1x^34+1x^36

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 1.27 seconds.