The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  X X^2  X X^2  0 X^2 X^2  1  1
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2  0 X^2+X  0  0 X^2 X^2+X  X X^2+X  X  0 X^2  X  X  X X^2  X  X X^2
 0  0  X  0  X  X X^2+X  0  0  0 X^2+X X^2+X  X  0 X^2  X X^2  0 X^2 X^2+X X^2  X  X  X  0  X X^2 X^2+X  X
 0  0  0  X  X  0 X^2+X  X X^2 X^2+X  X X^2 X^2 X^2 X^2+X  0  X X^2+X X^2  X  X X^2+X X^2  X  0 X^2+X X^2+X  X  0
 0  0  0  0 X^2  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0
 0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2
 0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2  0 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+59x^22+76x^23+158x^24+210x^25+290x^26+430x^27+515x^28+626x^29+523x^30+454x^31+298x^32+166x^33+137x^34+58x^35+49x^36+22x^37+14x^38+6x^39+3x^40+1x^42

The gray image is a linear code over GF(2) with n=116, k=12 and d=44.
This code was found by Heurico 1.16 in 0.386 seconds.