The generator matrix

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

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+2x^34+50x^35+3x^36+1x^38+6x^39+1x^42

The gray image is a linear code over GF(2) with n=280, k=6 and d=136.
This code was found by Heurico 1.16 in 0.016 seconds.