The generator matrix

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

generates a code of length 34 over Z2[X]/(X^4) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+159x^30+265x^32+1228x^34+234x^36+140x^38+10x^40+8x^42+1x^44+1x^46+1x^60

The gray image is a linear code over GF(2) with n=272, k=11 and d=120.
This code was found by Heurico 1.16 in 142 seconds.