The generator matrix

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

generates a code of length 25 over Z2[X]/(X^3) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+87x^16+304x^18+96x^19+642x^20+448x^21+1220x^22+1952x^23+1811x^24+3200x^25+1840x^26+1952x^27+1292x^28+448x^29+664x^30+96x^31+240x^32+64x^34+18x^36+4x^38+5x^40

The gray image is a linear code over GF(2) with n=100, k=14 and d=32.
This code was found by Heurico 1.16 in 3.5 seconds.