The generator matrix

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

generates a code of length 35 over Z2[X]/(X^4) who´s minimum homogenous weight is 33.

Homogenous weight enumerator: w(x)=1x^0+10x^33+18x^34+206x^35+6x^36+6x^37+4x^38+2x^39+1x^40+2x^50

The gray image is a linear code over GF(2) with n=280, k=8 and d=132.
This code was found by Heurico 1.16 in 0.031 seconds.