The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  X  1 X^3
 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 X^3+X^2 X^2+X  0  X X^3+X^2 X^3+X^2 X^3+X  X X^3+X^2+X X^3 X^3+X^2+X  0 X^2
 0  0 X^3+X^2  0 X^2 X^2 X^3 X^2 X^3 X^3 X^2 X^3+X^2 X^3+X^2 X^3 X^3 X^2  0 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^2
 0  0  0 X^3 X^3  0 X^3 X^3  0 X^3  0  0 X^3  0 X^3  0  0  0 X^3  0 X^3 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 22.

Homogenous weight enumerator: w(x)=1x^0+61x^22+92x^23+242x^24+288x^25+214x^26+48x^27+35x^28+16x^29+21x^30+4x^31+1x^32+1x^44

The gray image is a linear code over GF(2) with n=200, k=10 and d=88.
This code was found by Heurico 1.16 in 0.015 seconds.