The generator matrix

 1  0  1  1 X^2  1 X^2+X  1  1  1  1  X  1  1 X^3+X^2  1 X^3+X^2  1  1  1  0  1  1  1  X  1  X X^3+X^2+X X^2+X X^3 X^2  1  1  1  1
 0  1  1 X^2+X  1 X^2+X+1  1 X^2 X^3+X+1 X^3+X^2+1 X^3+X  1 X^2 X^3+X+1  1 X^3+X  1  1  X X+1  1 X^3+X^2 X^3+1 X^2+X  1 X^3+1 X^2+X  1  1 X^2  X X^3+X X^3+X^2 X^3+X  0
 0  0  X  0 X^3+X  X X^3 X^3+X X^3+X^2 X^2 X^2+X  X X^2+X X^3+X^2+X X^3+X^2+X X^3 X^3 X^2 X^3+X  0 X^3+X^2  0 X^3+X^2+X X^2 X^2+X X^3 X^3+X X^3+X^2 X^2+X  X X^2+X X^3+X^2 X^3+X^2 X^3+X^2 X^3
 0  0  0 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3  0  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+116x^31+289x^32+696x^33+581x^34+914x^35+539x^36+528x^37+183x^38+144x^39+56x^40+24x^41+11x^42+10x^43+3x^44+1x^46

The gray image is a linear code over GF(2) with n=280, k=12 and d=124.
This code was found by Heurico 1.16 in 0.125 seconds.