The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3+X  1  1 X^3+X^2  1  1  1  1  0 X^2+X  1  1  1  1 X^3+X^2 X^3+X  1  1  1  1  1
 0  1 X+1 X^2+X X^2+1  1 X^3+X^2 X^3+X^2+X+1  1 X^3+X X^3+1  1  0 X^2+X X+1 X^2+1  1  1 X^3+X^2 X^3+X X^3+X^2+X+1 X^3+1  1  1 X^3 X^3+X^2+X X^2  X  0
 0  0 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3  0

generates a code of length 29 over Z2[X]/(X^4) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+84x^27+62x^28+216x^29+62x^30+84x^31+1x^32+2x^42

The gray image is a linear code over GF(2) with n=232, k=9 and d=108.
This code was found by Heurico 1.16 in 3.81e-009 seconds.