The generator matrix

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

generates a code of length 35 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 33.

Homogenous weight enumerator: w(x)=1x^0+256x^33+172x^34+336x^35+28x^36+104x^37+52x^38+64x^39+2x^40+8x^41+1x^48

The gray image is a code over GF(2) with n=280, k=10 and d=132.
This code was found by Heurico 1.16 in 11 seconds.