The generator matrix

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

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+14x^33+94x^34+292x^35+95x^36+14x^37+1x^38+1x^66

The gray image is a code over GF(2) with n=280, k=9 and d=132.
This code was found by Heurico 1.16 in 0.031 seconds.