The generator matrix

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

generates a code of length 29 over Z2[X]/(X^3) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+170x^16+96x^18+160x^19+4x^20+36x^22+512x^23+520x^24+448x^25+696x^26+2912x^27+584x^28+4224x^29+544x^30+2912x^31+541x^32+448x^33+416x^34+512x^35+196x^36+180x^38+160x^39+16x^40+40x^42+16x^44+40x^46

The gray image is a linear code over GF(2) with n=116, k=14 and d=32.
This code was found by Heurico 1.16 in 3.75 seconds.