The generator matrix

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

generates a code of length 34 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+284x^31+794x^32+770x^33+824x^34+452x^35+507x^36+222x^37+135x^38+84x^39+10x^40+12x^41+1x^42

The gray image is a code over GF(2) with n=272, k=12 and d=124.
This code was found by Heurico 1.16 in 0.078 seconds.