The generator matrix
1 1 1 1 1 1 1 1 1 1 X 1 X 1 X X 1 X X^2 0 1 X X^2 X^3 X^2 X X X^2 1
0 X^3+X^2 X^3 X^2 0 X^3+X^2 X^3 X^2 0 X^3+X^2 X^3+X^2 X^3 X^2 X^2 0 X^3 0 X^3+X^2 X^3+X^2 X^2 X^3 X^2 X^2 X^2 X^3 0 X^3 0 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+3x^28+44x^29+3x^30+12x^31+1x^34
The gray image is a linear code over GF(2) with n=232, k=6 and d=112.
This code was found by Heurico 1.16 in -3.24e-008 seconds.