The generator matrix

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

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+80x^30+594x^31+1330x^32+1902x^33+2841x^34+2846x^35+3095x^36+1928x^37+1017x^38+466x^39+193x^40+58x^41+11x^42+14x^43+5x^44+3x^46

The gray image is a code over GF(2) with n=280, k=14 and d=120.
This code was found by Heurico 1.16 in 1.3 seconds.