The generator matrix

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

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+111x^16+16x^17+97x^18+208x^19+178x^20+736x^21+814x^22+2480x^23+1903x^24+3360x^25+1759x^26+2352x^27+844x^28+992x^29+324x^30+80x^31+32x^32+16x^33+63x^34+2x^36+14x^38+1x^40+1x^42

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 2.51 seconds.