The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+102x^31+337x^32+634x^33+690x^34+720x^35+654x^36+516x^37+246x^38+110x^39+28x^40+22x^41+24x^42+4x^43+4x^44+4x^45

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 0.125 seconds.