The generator matrix

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

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+93x^20+84x^21+239x^22+320x^23+527x^24+704x^25+1110x^26+1656x^27+2090x^28+2636x^29+2115x^30+1696x^31+1237x^32+732x^33+486x^34+280x^35+193x^36+64x^37+75x^38+16x^39+19x^40+4x^41+4x^42+3x^46

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 5.92 seconds.