The generator matrix

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

generates a code of length 25 over Z2[X]/(X^4) who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+64x^23+73x^24+264x^25+40x^26+48x^27+13x^28+8x^29+1x^44

The gray image is a linear code over GF(2) with n=200, k=9 and d=92.
This code was found by Heurico 1.16 in 0.016 seconds.