The generator matrix

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

generates a code of length 35 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+38x^34+42x^35+37x^36+4x^37+1x^38+2x^39+2x^40+1x^42

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 0.016 seconds.