The generator matrix

 1  0  0  1  1  1 X^3 X^2  0  1  1  1  X  1  1 X^3+X^2+X  1 X^3+X^2+X X^3+X  1 X^2 X^2+X X^2+X  1  1  1 X^3+X  1  1 X^3  1  1  X  1  1
 0  1  0  0 X^3+X^2+1 X^3+X^2+1  1  X  1 X^3+X^2  1 X^3+X^2+X  1 X^3+X+1  X X^3+X X+1  1  1 X^2+X+1  1  1 X^3  X X^3+1 X^3+1 X^3+X^2 X^3+X^2  X  1 X^3+X X^2  1 X^2 X^3+X^2
 0  0  1 X+1 X^2+X+1 X^2 X^2+X+1  1 X^2+X X^2+X  X  1 X^3+1 X^2+X+1 X+1  1 X^3+X^2+X X^2+X+1 X^3+X^2 X^3+X^2+1 X^2  X  1 X^3+X^2 X^3+X^2+X X^2+1  1  X X^3+X X^3+1 X^3+X^2 X^3+X^2 X^3+X^2+X+1 X+1  0
 0  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3  0 X^3 X^3 X^3  0  0  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3  0 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+168x^31+738x^32+1124x^33+1524x^34+1440x^35+1377x^36+808x^37+600x^38+264x^39+101x^40+20x^41+4x^42+16x^43+7x^44

The gray image is a linear code over GF(2) with n=280, k=13 and d=124.
This code was found by Heurico 1.16 in 0.657 seconds.