The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X^2 1 X^2 X 0 1 X^2 1 X X X X
0 X 0 0 0 0 0 0 0 X X^2+X X X X^2+X X X^2 X^2 X^2+X X 0 0 X^2+X X X X^2+X X X X^2+X
0 0 X 0 0 0 X X^2+X X 0 0 0 X X X^2+X X^2 X X X^2 X X X^2 X X^2 X 0 X^2 X
0 0 0 X 0 X X X^2+X 0 X X X^2 0 X^2 X^2+X X 0 X X^2 X X^2+X X^2+X X^2+X X 0 X X^2 X
0 0 0 0 X X 0 X^2+X X X^2 X^2+X X^2+X 0 X^2+X X X^2+X X^2+X 0 X X^2 X 0 X X X X^2 X^2+X X^2
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 0 X^2 X^2 0 X^2 X^2 X^2
0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 0 X^2 X^2
0 0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 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+224x^20+590x^22+120x^23+1380x^24+704x^25+2344x^26+1112x^27+3102x^28+1472x^29+2532x^30+552x^31+1372x^32+128x^33+520x^34+8x^35+184x^36+30x^38+6x^40+2x^44+1x^48
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 5.62 seconds.