The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  X  1  X  X  1  X  X  X  X  1  1  1  X  1  1  1  1  X
 0 X^2  0  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2
 0  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2  0
 0  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  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+18x^28+32x^29+6x^30+4x^32+2x^38+1x^40

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 0.00577 seconds.