The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  1  X  X  X X^2
 0 X^3  0  0  0  0  0 X^3  0  0 X^3 X^3  0  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3
 0  0 X^3  0  0  0  0 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3
 0  0  0 X^3  0  0  0 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0  0  0 X^3  0 X^3 X^3
 0  0  0  0 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3
 0  0  0  0  0 X^3 X^3  0  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3 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+12x^21+21x^22+88x^24+296x^25+64x^26+12x^29+10x^30+7x^32+1x^38

The gray image is a linear code over GF(2) with n=200, k=9 and d=84.
This code was found by Heurico 1.16 in 0.141 seconds.