The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  1  1  1  1  1 X^2 X^2  1  1  X
 0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^2 X^3 X^3+X^2  0 X^3+X^2 X^3 X^3+X^2 X^3+X^2  0  0  0 X^3 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2  0
 0  0 X^3  0  0  0  0  0 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0  0  0 X^3 X^3 X^3  0 X^3
 0  0  0 X^3  0  0  0 X^3  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0  0
 0  0  0  0 X^3  0  0  0  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3
 0  0  0  0  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3  0  0 X^3  0 X^3  0  0 X^3  0 X^3
 0  0  0  0  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3  0 X^3  0  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 20.

Homogenous weight enumerator: w(x)=1x^0+72x^20+72x^22+256x^23+130x^24+1024x^25+80x^26+256x^27+100x^28+40x^30+11x^32+4x^36+2x^40

The gray image is a linear code over GF(2) with n=200, k=11 and d=80.
This code was found by Heurico 1.16 in 0.047 seconds.