The generator matrix

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

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+110x^35+6x^36+1x^38+1x^40+2x^43+1x^46

The gray image is a code over GF(2) with n=280, k=7 and d=136.
This code was found by Heurico 1.16 in 0.031 seconds.