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

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+10x^27+47x^28+396x^29+47x^30+10x^31+1x^58

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 0.015 seconds.