The generator matrix

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

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+342x^30+1100x^31+2435x^32+3772x^33+5816x^34+6104x^35+5679x^36+3704x^37+2338x^38+940x^39+366x^40+108x^41+40x^42+16x^43+7x^44

The gray image is a linear code over GF(2) with n=280, k=15 and d=120.
This code was found by Heurico 1.16 in 5.87 seconds.