The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  1  1  1  1  1  1  1  1  1  1  1  1 X^2  X  1
 0 X^3+X^2  0  0  0 X^2 X^3+X^2 X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3+X^2 X^3 X^2 X^3  0 X^2 X^3+X^2 X^2 X^3 X^3+X^2  0 X^3+X^2 X^2 X^3+X^2 X^2 X^2 X^3
 0  0 X^3+X^2  0 X^2 X^2 X^2 X^3  0 X^3 X^2 X^3+X^2 X^2 X^2 X^3 X^3 X^2 X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^3 X^3  0 X^3 X^2 X^3 X^3 X^2 X^3+X^2 X^3+X^2
 0  0  0 X^3+X^2 X^2 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3 X^3+X^2 X^2  0 X^3+X^2  0 X^3+X^2 X^2 X^2 X^2  0 X^3+X^2  0 X^2  0 X^3 X^3 X^2 X^3+X^2 X^3  0 X^3 X^3 X^3 X^3
 0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3  0  0  0  0  0  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3  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+70x^31+102x^32+34x^33+500x^34+576x^35+501x^36+28x^37+72x^38+46x^39+25x^40+2x^41+15x^42+12x^43+11x^44+2x^46+1x^58

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 0.078 seconds.