The generator matrix

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

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+53x^30+56x^31+105x^32+64x^33+234x^34+1048x^35+238x^36+64x^37+86x^38+40x^39+34x^40+6x^42+8x^43+2x^44+4x^46+4x^48+1x^62

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 114 seconds.