The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+87x^30+380x^31+633x^32+668x^33+808x^34+500x^35+522x^36+300x^37+79x^38+48x^39+43x^40+24x^41+2x^42+1x^48

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 0.11 seconds.