The generator matrix

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

generates a code of length 29 over Z2[X]/(X^3) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+34x^26+130x^27+93x^28+86x^29+53x^30+28x^31+30x^32+30x^33+7x^34+14x^35+4x^36+2x^38

The gray image is a linear code over GF(2) with n=116, k=9 and d=52.
This code was found by Heurico 1.11 in 6.87e-008 seconds.