The generator matrix

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

generates a code of length 28 over Z2[X]/(X^3) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+174x^16+78x^19+264x^20+112x^21+252x^22+914x^23+772x^24+1376x^25+408x^26+3884x^27+208x^28+3072x^29+788x^30+1988x^31+457x^32+544x^33+336x^34+294x^35+168x^36+16x^37+228x^38+10x^39+4x^40+24x^42+12x^46

The gray image is a linear code over GF(2) with n=112, k=14 and d=32.
This code was found by Heurico 1.16 in 3.63 seconds.