The generator matrix

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

generates a code of length 25 over Z2[X]/(X^4) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+2x^24+48x^25+3x^26+8x^27+1x^28+1x^30

The gray image is a linear code over GF(2) with n=200, k=6 and d=96.
This code was found by Heurico 1.16 in 6.87e-008 seconds.