The generator matrix

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

generates a code of length 35 over Z2[X]/(X^4) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+122x^32+248x^34+256x^35+336x^36+8x^38+52x^40+1x^64

The gray image is a linear code over GF(2) with n=280, k=10 and d=128.
This code was found by Heurico 1.16 in 0.031 seconds.