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

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+39x^32+296x^33+39x^34+368x^35+20x^36+200x^37+12x^38+4x^40+32x^41+12x^42+1x^66

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.