The generator matrix

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

generates a code of length 25 over Z2[X]/(X^3) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+192x^18+706x^19+1555x^20+2884x^21+5240x^22+6966x^23+9794x^24+10436x^25+10162x^26+7390x^27+5126x^28+2700x^29+1484x^30+586x^31+225x^32+76x^33+10x^34+3x^36

The gray image is a linear code over GF(2) with n=100, k=16 and d=36.
This code was found by Heurico 1.13 in 13.4 seconds.