The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+6x^34+44x^35+6x^36+4x^39+1x^40+2x^42

The gray image is a code over GF(2) with n=280, k=6 and d=136.
This code was found by Heurico 1.16 in -3.24e-008 seconds.