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

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+31x^32+448x^35+31x^38+1x^70

The gray image is a linear code over GF(2) with n=280, k=9 and d=128.
This code was found by Heurico 1.16 in 0.031 seconds.