The generator matrix

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

generates a code of length 29 over Z2[X]/(X^4) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+6x^28+108x^29+6x^30+1x^32+4x^33+2x^34

The gray image is a linear code over GF(2) with n=232, k=7 and d=112.
This code was found by Heurico 1.16 in 1.05e-007 seconds.