The generator matrix

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

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+21x^22+128x^23+227x^24+434x^25+602x^26+1024x^27+932x^28+1420x^29+984x^30+1060x^31+585x^32+436x^33+174x^34+88x^35+44x^36+12x^37+11x^38+4x^39+3x^40+2x^41

The gray image is a linear code over GF(2) with n=116, k=13 and d=44.
This code was found by Heurico 1.16 in 0.899 seconds.