The generator matrix

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

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+64x^21+68x^22+174x^23+518x^24+450x^25+515x^26+132x^27+20x^28+60x^29+24x^30+14x^31+5x^32+2x^33+1x^42

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.