The generator matrix

 1  0  0  1  1  1 X^3  X  1  1 X^2+X  1  1 X^2+X  1  1 X^3+X X^3+X^2+X  1  1 X^3+X^2+X  1  1  1  0  1  X X^3+X X^3  1  1 X^3+X^2 X^3+X^2  1  1
 0  1  0  X X^3+1 X+1  1  1 X^3+X  X  1 X^3+X^2+X+1 X^3+X^2+1 X^3 X^2 X^3+X^2+X+1  X  1 X^2+1 X^2  1 X^3 X^3+X+1 X^3+X^2  1 X+1  0  1  1 X^2+X  0  1  1  X  0
 0  0  1  1  1  0 X+1 X^3+X X^3 X^2+X+1 X+1  X X^3+X^2+X+1  1 X^3+X^2+X X^3+X^2+1  1 X^3+X^2 X^3+X X+1  1 X^3+1 X^3+X^2+X X^3 X^2+1 X^3+X^2+X+1  1 X+1 X^2+X X^2+1 X^3+X X^3+X^2+X+1 X^2+1  1  0
 0  0  0 X^2 X^3+X^2 X^3 X^2 X^3  0 X^3  0 X^3+X^2 X^3+X^2  0 X^2 X^3 X^3+X^2 X^3+X^2 X^2 X^3 X^3 X^3  0 X^3+X^2 X^2 X^2 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2  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+130x^30+574x^31+1305x^32+2228x^33+2387x^34+3192x^35+2576x^36+2136x^37+1051x^38+506x^39+192x^40+48x^41+29x^42+16x^43+4x^44+4x^45+3x^46+2x^48

The gray image is a linear code over GF(2) with n=280, k=14 and d=120.
This code was found by Heurico 1.16 in 1.56 seconds.