The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  X  X  0 X^2  X  1  1  1  1 X^2  X  X
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2  X X^2+X X^2+X  0 X^2  X  0  X  X  0  X X^2+X  X  X  0 X^2+X  X
 0  0  X  0  X  X X^2+X  0  0  0  X X^2  X  X X^2+X X^2+X X^2  X X^2  X  0 X^2  X  0 X^2+X  X  X X^2+X
 0  0  0  X  X  0 X^2+X  X  0  X  0  X X^2+X  X X^2  X X^2+X X^2+X  0 X^2 X^2+X X^2+X  0 X^2  0  0 X^2+X X^2
 0  0  0  0 X^2  0  0  0  0 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  0 X^2 X^2
 0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0
 0  0  0  0  0  0 X^2  0  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2
 0  0  0  0  0  0  0 X^2  0  0  0  0 X^2  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 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0 X^2  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+253x^20+572x^22+96x^23+1371x^24+608x^25+2336x^26+1344x^27+3126x^28+1344x^29+2472x^30+608x^31+1433x^32+96x^33+480x^34+201x^36+28x^38+11x^40+4x^44

The gray image is a linear code over GF(2) with n=112, k=14 and d=40.
This code was found by Heurico 1.16 in 6.33 seconds.