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.