The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+121x^28+996x^29+3154x^30+8242x^31+16684x^32+31494x^33+44034x^34+51824x^35+44953x^36+32216x^37+16370x^38+7922x^39+2885x^40+854x^41+278x^42+76x^43+26x^44+8x^45+4x^46+2x^48

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 251 seconds.