The generator matrix

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

generates a code of length 35 over Z2[X]/(X^4) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+6x^34+110x^35+6x^36+1x^38+1x^40+2x^43+1x^46

The gray image is a linear code over GF(2) with n=280, k=7 and d=136.
This code was found by Heurico 1.16 in 0.016 seconds.