The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+48x^34+14x^36+1x^40

The gray image is a code over GF(2) with n=272, k=6 and d=136.
This code was found by Heurico 1.16 in 0.015 seconds.