The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0 X^3+X^2  0 X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^2 X^2 X^3 X^3 X^2  0 X^2 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^3 X^3 X^3 X^3+X^2  0
 0  0 X^3+X^2 X^2  0 X^2 X^2 X^3 X^3 X^2 X^3 X^2 X^3 X^3+X^2 X^3+X^2  0  0 X^3+X^2 X^3 X^3+X^2 X^3+X^2  0  0 X^3+X^2  0
 0  0  0 X^3 X^3 X^3  0 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0  0  0  0 X^3 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+14x^22+24x^23+17x^24+400x^25+17x^26+24x^27+14x^28+1x^50

The gray image is a linear code over GF(2) with n=200, k=9 and d=88.
This code was found by Heurico 1.16 in 0.016 seconds.