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.