The generator matrix

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

generates a code of length 28 over Z2[X]/(X^3) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+46x^20+26x^21+93x^22+122x^23+327x^24+122x^25+652x^26+282x^27+858x^28+158x^29+644x^30+190x^31+279x^32+78x^33+130x^34+46x^35+24x^36+15x^38+1x^40+2x^42

The gray image is a linear code over GF(2) with n=112, k=12 and d=40.
This code was found by Heurico 1.16 in 0.342 seconds.