The generator matrix

 1  0  0  0  1  1  1 X^2  1  1 X^3+X  X X^3+X  1  1  0  1 X^2  1 X^3+X^2+X  X  1  1 X^3+X^2+X  1
 0  1  0  0 X^2 X^3+1  1  1 X^2+1 X^3+1 X^3+X^2  1  1 X^3  X X^3+X^2+X X^2+X  1 X^3+X^2  1  1 X^3+X^2+X+1 X^2+X+1  1 X^2
 0  0  1  0 X^2+1  1 X^2 X^2+1 X+1 X^2+X  1 X^2 X+1 X^3+X^2 X^3+X^2 X^3+X X^2+1  X  1 X^2+1  X X^3+X+1 X^3+1 X^3+X^2+X X^3+X^2
 0  0  0  1  1 X^2 X^2+1 X^3+1 X+1 X^2+X X^3+1 X^2+X+1  0 X^3+X^2+X+1  X  1 X^3+X^2 X^3 X^2+X+1 X^3+X X+1 X^3+X  1 X^2 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+226x^20+1278x^21+3809x^22+7420x^23+11835x^24+15850x^25+12746x^26+7570x^27+3274x^28+1090x^29+357x^30+64x^31+6x^32+6x^33+2x^35+2x^36

The gray image is a linear code over GF(2) with n=200, k=16 and d=80.
This code was found by Heurico 1.16 in 14.3 seconds.