The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3+X^2  1  1 X^3+X  1  1  0  1  1 X^2+X  1  1  0  1  1 X^2+X  X  X  0  X  1  1 X^3+X  1  1 X^3+X^2  1
 0  1 X+1 X^2+X X^2+1  1 X^3+X^2+X+1 X^3+X^2  1 X^3+X X^3+1  1  0 X+1  1 X^2+X X^2+1  1  0 X+1  1 X^2+X X^2+1  1  0 X^2+X  X X^3 X^3+X^2 X^3+X+1  1 X^3+X^2 X^3+X^2+X+1  1 X+1
 0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3  0  0  0 X^3 X^3  0  0
 0  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3  0  0  0 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3  0
 0  0  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3  0  0 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+80x^31+169x^32+200x^33+484x^34+224x^35+456x^36+184x^37+152x^38+64x^39+14x^40+16x^41+3x^42+1x^58

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 0.031 seconds.