The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  0  1  1 X^3  1  0  1 X^2  1  1  X  1  1
 0  X  0 X^3+X^2+X X^3 X^2+X  0  X X^2 X^3+X^2+X X^3+X^2 X^3+X  X X^3+X^2 X^3+X^2  X X^3+X^2+X  X  X  X X^2+X X^3 X^2+X X^2+X X^3
 0  0 X^3+X^2  0 X^3 X^3+X^2 X^3+X^2 X^2 X^2 X^2 X^3 X^2 X^3  0 X^2 X^3+X^2  0 X^3+X^2 X^3  0  0 X^2 X^3+X^2 X^3+X^2  0
 0  0  0 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3  0  0 X^3+X^2 X^3+X^2 X^3 X^3 X^2 X^3 X^3 X^2 X^2 X^3+X^2  0 X^3 X^3+X^2 X^3+X^2 X^3+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+28x^21+161x^22+176x^23+482x^24+378x^25+494x^26+152x^27+122x^28+24x^29+13x^30+8x^31+2x^32+2x^33+4x^34+1x^40

The gray image is a linear code over GF(2) with n=200, k=11 and d=84.
This code was found by Heurico 1.16 in 0.047 seconds.