The generator matrix

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

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+52x^30+132x^31+343x^32+460x^33+779x^34+690x^35+783x^36+338x^37+239x^38+136x^39+86x^40+32x^41+15x^42+2x^43+3x^44+2x^45+2x^46+1x^54

The gray image is a linear code over GF(2) with n=280, k=12 and d=120.
This code was found by Heurico 1.16 in 0.157 seconds.