The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2  0  X X^2  1  1  1  X  0  1  1
 0  X  0  0  0  0  0  0  0  X X^2+X  X X^2 X^2  X  0 X^2 X^2+X  X  X  0  X X^2+X X^2+X X^2 X^2  0 X^2+X X^2
 0  0  X  0  0  0  X X^2+X  X  X  X  0  0  X X^2  X X^2+X X^2+X X^2  0  0  X X^2 X^2  X X^2 X^2  0  0
 0  0  0  X  0  X  X  X X^2  0  0 X^2 X^2 X^2 X^2+X X^2+X  0  X X^2+X X^2+X  X X^2 X^2+X X^2+X X^2  0  0  0  X
 0  0  0  0  X  X X^2 X^2+X X^2+X  0  X  X  0 X^2+X  X X^2  X X^2+X X^2 X^2+X  X X^2 X^2+X X^2+X X^2 X^2+X  X X^2  0
 0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  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+43x^22+80x^23+150x^24+202x^25+283x^26+428x^27+556x^28+620x^29+560x^30+454x^31+269x^32+194x^33+117x^34+56x^35+48x^36+8x^37+20x^38+6x^39+1x^46

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 0.388 seconds.