The generator matrix

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

generates a code of length 29 over Z2[X]/(X^3) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+398x^22+884x^23+2109x^24+3008x^25+5595x^26+6588x^27+8981x^28+9612x^29+9804x^30+6904x^31+5624x^32+2968x^33+1904x^34+636x^35+339x^36+92x^37+58x^38+28x^39+2x^40+1x^42

The gray image is a linear code over GF(2) with n=116, k=16 and d=44.
This code was found by Heurico 1.13 in 17.3 seconds.