The generator matrix

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

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+9x^26+12x^27+22x^28+168x^29+22x^30+12x^31+9x^32+1x^58

The gray image is a linear code over GF(2) with n=116, k=8 and d=52.
This code was found by Heurico 1.16 in 0.0097 seconds.