The generator matrix

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

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+132x^20+692x^21+1874x^22+3656x^23+6424x^24+7150x^25+6659x^26+3520x^27+1816x^28+666x^29+108x^30+56x^31+3x^32+2x^33+7x^34+2x^37

The gray image is a linear code over GF(2) with n=200, k=15 and d=80.
This code was found by Heurico 1.16 in 3.69 seconds.