The generator matrix

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

generates a code of length 34 over Z2[X]/(X^4) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+212x^31+281x^32+404x^33+394x^34+336x^35+157x^36+168x^37+53x^38+12x^39+8x^40+20x^41+1x^44+1x^46

The gray image is a linear code over GF(2) with n=272, k=11 and d=124.
This code was found by Heurico 1.16 in 0.046 seconds.