The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+782x^30+2396x^31+4431x^32+8012x^33+10992x^34+12444x^35+10955x^36+8016x^37+4498x^38+2076x^39+666x^40+196x^41+40x^42+12x^43+19x^44

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 17.8 seconds.