The generator matrix

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

Homogenous weight enumerator: w(x)=1x^0+124x^22+32x^23+269x^24+192x^25+288x^26+32x^27+48x^28+28x^30+1x^32+8x^34+1x^40

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 23.2 seconds.