The generator matrix

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

generates a code of length 35 over Z2[X]/(X^4) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+281x^32+192x^33+356x^34+384x^35+392x^36+192x^37+216x^38+28x^40+4x^42+2x^48

The gray image is a linear code over GF(2) with n=280, k=11 and d=128.
This code was found by Heurico 1.16 in 0.063 seconds.