The generator matrix

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

generates a code of length 35 over Z2[X]/(X^4) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+88x^31+200x^32+164x^33+432x^34+280x^35+515x^36+144x^37+80x^38+80x^39+42x^40+12x^41+9x^44+1x^56

The gray image is a linear code over GF(2) with n=280, k=11 and d=124.
This code was found by Heurico 1.16 in 32 seconds.