The generator matrix

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

generates a code of length 29 over Z2[X]/(X^3) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+170x^20+350x^22+1156x^24+2354x^26+4211x^28+3924x^30+2712x^32+972x^34+400x^36+78x^38+50x^40+2x^42+3x^44+1x^48

The gray image is a linear code over GF(2) with n=116, k=14 and d=40.
This code was found by Heurico 1.16 in 5.54 seconds.