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

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+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 0.015 seconds.