The generator matrix

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

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+313x^32+536x^33+666x^34+776x^35+662x^36+556x^37+224x^38+112x^39+46x^40+24x^41+4x^42+2x^44+4x^45+2x^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 18.8 seconds.