The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  X  1  1  X  X  X  X  X  X  X  X  X  1
 0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^3+X^2 X^3 X^2 X^3 X^2 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3 X^3 X^3 X^2  0  0 X^3 X^3+X^2 X^2 X^2 X^2  0 X^3+X^2
 0  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0  0  0 X^3 X^3  0 X^3 X^3  0  0  0
 0  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3  0 X^3  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3  0  0  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+14x^27+12x^28+208x^29+12x^30+3x^32+4x^34+2x^43

The gray image is a linear code over GF(2) with n=232, k=8 and d=108.
This code was found by Heurico 1.16 in 2.26 seconds.