The generator matrix

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

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+154x^31+329x^32+614x^33+574x^34+814x^35+592x^36+558x^37+255x^38+146x^39+34x^40+10x^41+1x^42+2x^43+4x^44+2x^45+1x^46+4x^47+1x^50

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 0.438 seconds.