The generator matrix

 1  0  1  1 X^2  1 X^2+X  1  1  1  1  X  1  1 X^3+X  1  1  1  0 X^3  X X^3+X^2  0 X^3  1
 0  1  1 X^2+X  1 X^2+X+1  1 X^2 X^3+X+1 X^3+X^2+1 X^3+X  1 X^2 X^3+X+1  1  X X^3+1  X  1  1  1  X  X  1 X^2+X+1
 0  0  X  0 X^3+X  X X^3 X^3+X X^3+X^2 X^2 X^2+X  X X^2+X X^3+X^2+X X^2+X X^3+X X^3+X^2+X X^3  0 X^3+X  0 X^3+X  X X^3+X^2 X^2
 0  0  0 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3  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+271x^22+636x^23+729x^24+984x^25+661x^26+488x^27+210x^28+56x^29+33x^30+12x^31+12x^32+3x^34

The gray image is a linear code over GF(2) with n=200, k=12 and d=88.
This code was found by Heurico 1.16 in 1.25 seconds.