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

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

Homogenous weight enumerator: w(x)=1x^0+52x^34+6x^36+4x^38+1x^40

The gray image is a code over GF(2) with n=136, k=6 and d=68.
This code was found by Heurico 1.16 in 0.00665 seconds.