The generator matrix

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

generates a code of length 34 over Z2[X]/(X^4) who´s minimum homogenous weight is 33.

Homogenous weight enumerator: w(x)=1x^0+18x^33+85x^34+18x^35+2x^37+2x^39+1x^42+1x^44

The gray image is a linear code over GF(2) with n=272, k=7 and d=132.
This code was found by Heurico 1.16 in 6.87e-008 seconds.