The generator matrix

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

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+56x^34+2x^36+4x^38+1x^48

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 0.14 seconds.