The generator matrix

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

generates a code of length 35 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+133x^28+900x^29+3321x^30+7806x^31+17714x^32+30392x^33+45169x^34+49926x^35+47107x^36+30412x^37+17709x^38+7498x^39+2669x^40+976x^41+295x^42+82x^43+24x^44+8x^45+2x^46

The gray image is a code over GF(2) with n=280, k=18 and d=112.
This code was found by Heurico 1.16 in 266 seconds.