The generator matrix

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

generates a code of length 35 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+93x^34+94x^35+35x^36+12x^37+15x^38+6x^39

The gray image is a code over GF(2) with n=280, k=8 and d=136.
This code was found by Heurico 1.16 in 3.62e-008 seconds.