The generator matrix

 1  0  0  0  1  1  1  1 X^3+X  1  X X^3  1 X^3+X  1  1  X  1 X^3 X^2  1  1  1  1 X^2+X
 0  1  0  0  0 X^3 X^2+1 X^3+X+1  1 X^3+1  1 X^3+X X^2+X+1  1 X^3+X X^2+1 X^3+X^2 X^3+X^2+X  0  1 X^3+X^2 X^2+X X^3+1 X^2  1
 0  0  1  0  1 X^3+X^2+X X^2  X  X  1 X^2+1  1 X^3+X+1 X^2+X+1 X^2+1 X^3+X^2+X+1  0 X^3+X^2+X  1 X^2+X X+1  0 X^2 X^3+X X+1
 0  0  0  1  1 X+1 X^2+X+1 X^3 X+1  X X^3+1 X^2+X+1 X^2+1  X X^3 X^2  1 X^3+1 X+1 X^3+X+1 X^3+X+1 X^2+X X^3+1 X^3 X^3+X^2
 0  0  0  0 X^3  0  0  0  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3 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+697x^20+2484x^21+6952x^22+14748x^23+25485x^24+29992x^25+25990x^26+14936x^27+6709x^28+2276x^29+684x^30+76x^31+34x^32+6x^34+2x^36

The gray image is a linear code over GF(2) with n=200, k=17 and d=80.
This code was found by Heurico 1.16 in 86.9 seconds.