The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  X  1  X  X  1  X  X  1  0  X  1  0  1  0  0  1  1  1
 0  X  0  0  0  X X^2+X  X  0 X^2  X X^2+X X^2+X  X X^2  X X^2+X X^2 X^2+X  X X^2  0  0 X^2+X  X  X  X  0  0
 0  0  X  0  X  X X^2+X  0  0  0  0  0 X^2  X  0  X  X X^2+X X^2 X^2+X X^2+X X^2 X^2  X  0  0 X^2+X  0  0
 0  0  0  X  X  0 X^2+X  X  0  X X^2+X X^2  X X^2  X  0  X  X X^2 X^2+X  X  0  X  X 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  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0
 0  0  0  0  0 X^2  0  0  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2
 0  0  0  0  0  0 X^2  0  0  0  0 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0
 0  0  0  0  0  0  0 X^2  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0
 0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2 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+92x^20+456x^22+48x^23+800x^24+352x^25+1946x^26+976x^27+2736x^28+1344x^29+3036x^30+976x^31+1895x^32+352x^33+864x^34+48x^35+336x^36+92x^38+24x^40+6x^42+4x^44

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 5.65 seconds.