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

generates a code of length 35 over Z2[X]/(X^4) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+50x^30+36x^31+117x^32+268x^33+99x^34+760x^35+468x^36+40x^37+98x^38+36x^39+54x^40+12x^41+8x^42+1x^66

The gray image is a linear code over GF(2) with n=280, k=11 and d=120.
This code was found by Heurico 1.16 in 0.062 seconds.