The generator matrix

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

generates a code of length 35 over Z2[X]/(X^4) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+102x^31+160x^32+330x^33+230x^34+442x^35+219x^36+314x^37+148x^38+72x^39+1x^40+10x^41+6x^42+6x^43+1x^44+2x^45+2x^47+2x^48

The gray image is a linear code over GF(2) with n=280, k=11 and d=124.
This code was found by Heurico 1.16 in 0.094 seconds.