The generator matrix

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

generates a code of length 25 over Z2[X]/(X^3) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+460x^20+160x^22+1637x^24+800x^26+908x^28+129x^32+1x^40

The gray image is a linear code over GF(2) with n=100, k=12 and d=40.
This code was found by Heurico 1.16 in 65.3 seconds.