The generator matrix

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

generates a code of length 34 over Z2[X]/(X^4) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+42x^28+96x^30+348x^32+1088x^34+334x^36+96x^38+34x^40+7x^44+1x^48+1x^60

The gray image is a linear code over GF(2) with n=272, k=11 and d=112.
This code was found by Heurico 1.16 in 0.078 seconds.