The generator matrix

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

generates a code of length 35 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+794x^30+2452x^31+4565x^32+7808x^33+10696x^34+12488x^35+11157x^36+8304x^37+4400x^38+1892x^39+694x^40+208x^41+68x^42+5x^44+2x^46+2x^48

The gray image is a code over GF(2) with n=280, k=16 and d=120.
This code was found by Heurico 1.16 in 17.3 seconds.