The generator matrix

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

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+190x^30+112x^31+770x^32+400x^33+1172x^34+400x^35+758x^36+112x^37+164x^38+4x^40+4x^42+2x^44+6x^46+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 86.9 seconds.