The generator matrix

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

generates a code of length 35 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+278x^31+170x^32+584x^33+613x^34+910x^35+598x^36+520x^37+122x^38+196x^39+26x^40+64x^41+1x^42+6x^43+4x^44+2x^47+1x^56

The gray image is a code over GF(2) with n=280, k=12 and d=124.
This code was found by Heurico 1.16 in 81.4 seconds.