The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  0  1  1  X  0  1  1  1  X  1  1  1  X  X  X  1
 0  X  0 X^2+X  0 X^2+X  0 X^2+X X^2 X^2+X  0 X^2+X X^2+X  X  0 X^2+X X^2+X  X  0  0  0 X^2+X X^2 X^2  X X^2+X X^2+X X^2+X X^2+X
 0  0 X^2  0  0  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0
 0  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0
 0  0  0  0 X^2  0  0  0  0  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2
 0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2
 0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2
 0  0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0  0 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+28x^22+36x^23+64x^24+120x^25+82x^26+348x^27+92x^28+528x^29+88x^30+348x^31+71x^32+120x^33+44x^34+36x^35+20x^36+12x^38+8x^40+2x^42

The gray image is a linear code over GF(2) with n=116, k=11 and d=44.
This code was found by Heurico 1.16 in 0.116 seconds.