The generator matrix

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

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+298x^32+152x^33+456x^34+344x^35+410x^36+136x^37+152x^38+8x^39+71x^40+16x^42+2x^44+1x^48+1x^56

The gray image is a linear code over GF(2) with n=280, k=11 and d=128.
This code was found by Heurico 1.16 in 24.4 seconds.