The generator matrix

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

generates a code of length 34 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+306x^30+48x^31+783x^32+336x^33+1288x^34+336x^35+611x^36+48x^37+246x^38+76x^40+12x^42+4x^46+1x^52

The gray image is a code over GF(2) with n=272, k=12 and d=120.
This code was found by Heurico 1.16 in 0.906 seconds.