The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+6x^34+42x^35+5x^36+4x^37+1x^38+2x^39+2x^40+1x^42

The gray image is a code over GF(2) with n=140, k=6 and d=68.
This code was found by Heurico 1.16 in 0.0073 seconds.