The generator matrix

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

generates a code of length 29 over Z2[X]/(X^3) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+56x^27+41x^28+88x^29+8x^30+40x^31+12x^32+8x^33+1x^36+1x^48

The gray image is a linear code over GF(2) with n=116, k=8 and d=54.
This code was found by Heurico 1.16 in 0.0072 seconds.