The generator matrix

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

generates a code of length 34 over Z2[X]/(X^4) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+270x^32+216x^33+212x^34+88x^35+107x^36+72x^37+44x^38+8x^39+3x^40+1x^44+2x^48

The gray image is a linear code over GF(2) with n=272, k=10 and d=128.
This code was found by Heurico 1.16 in 1.53 seconds.