The generator matrix

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

generates a code of length 25 over Z2[X]/(X^4) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+12x^22+52x^24+128x^25+48x^26+8x^28+4x^30+3x^32

The gray image is a linear code over GF(2) with n=200, k=8 and d=88.
This code was found by Heurico 1.16 in -3.24e-008 seconds.