The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  1  1  1  X  1  1  1  1  1  1  1
 0 X^2  0  0  0  0  0  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 X^2
 0  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 X^2  0  0 X^2 X^2
 0  0  0 X^2  0  0  0  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0
 0  0  0  0 X^2  0  0  0  0  0  0  0  0 X^2 X^2 X^2  0  0 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  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0
 0  0  0  0  0  0 X^2  0  0  0  0  0 X^2 X^2  0  0 X^2 X^2 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  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0
 0  0  0  0  0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0
 0  0  0  0  0  0  0  0  0 X^2  0  0 X^2  0 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  0 X^2  0 X^2 X^2  0 X^2  0  0 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 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  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+181x^16+404x^20+1076x^24+1024x^26+10980x^28+1024x^30+1143x^32+380x^36+156x^40+12x^44+3x^48

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 3.82 seconds.