The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+6x^33+15x^34+210x^35+15x^36+6x^37+1x^38+2x^51

The gray image is a code over GF(2) with n=280, k=8 and d=132.
This code was found by Heurico 1.16 in 0.016 seconds.