The generator matrix
1 1 1 1 1 1 1 1 1 1 X 0 1 1 X 0 1 X X 1 X X^2 X X^2 1 1 X X 1
0 X 0 X^2+X X^2 X^2+X X^2 X 0 X^2+X X^2+X X 0 X^2+X X^2+X X X^2 0 X^2 X X X X X X^2 X 0 X^2 0
0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0
generates a code of length 29 over Z2[X]/(X^3) who´s minimum homogenous weight is 28.
Homogenous weight enumerator: w(x)=1x^0+6x^28+44x^29+6x^30+1x^32+4x^33+2x^34
The gray image is a linear code over GF(2) with n=116, k=6 and d=56.
This code was found by Heurico 1.16 in 0.00752 seconds.