The generator matrix

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

generates a code of length 35 over Z2[X]/(X^4) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+330x^32+824x^33+603x^34+912x^35+387x^36+592x^37+251x^38+80x^39+81x^40+24x^41+9x^42+1x^44+1x^46

The gray image is a linear code over GF(2) with n=280, k=12 and d=128.
This code was found by Heurico 1.16 in 0.328 seconds.