The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3+X^2  1  1 X^3+X  1  1  1  1  0  1 X^2+X  1  1  1 X^2+X  0  1
 0  1 X+1 X^2+X X^2+1  1 X^3+X^2 X^3+X^2+X+1  1 X^3+X X^3+1  1  0 X^2+X  0 X+1  1 X^2+1  1 X^3+X X^3+1 X+1  1  1  0
 0  0 X^3  0  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0  0  0 X^3 X^3  0  0  0
 0  0  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3  0  0  0
 0  0  0  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3  0  0
 0  0  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0 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 20.

Homogenous weight enumerator: w(x)=1x^0+24x^20+76x^21+159x^22+544x^23+844x^24+808x^25+846x^26+544x^27+152x^28+76x^29+8x^30+3x^32+10x^34+1x^38

The gray image is a linear code over GF(2) with n=200, k=12 and d=80.
This code was found by Heurico 1.16 in 0.078 seconds.