The generator matrix

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

generates a code of length 25 over Z2[X]/(X^4) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+30x^20+128x^21+234x^22+356x^23+751x^24+1100x^25+810x^26+352x^27+164x^28+80x^29+43x^30+28x^31+14x^32+4x^33+1x^38

The gray image is a linear code over GF(2) with n=200, k=12 and d=80.
This code was found by Heurico 1.16 in 0.125 seconds.