The generator matrix

 1  0  1  1  1 X+2  1  1 2X+2  1  1 3X  1  1  0  1  1 X+2  1  1  1 3X  1  1 2X+2  1  0  1 2X+2  1  1  1  1  1
 0  1 X+1 X+2  3  1 2X+2 3X+3  1 3X 2X+1  1  0 X+1  1 X+2  3  1 2X+2 3X+3 3X  1  0 2X+1  1 2X+1  1  3  1 X+1  3 2X+2 X+1 2X+1
 0  0 2X  0  0  0  0 2X  0 2X 2X 2X  0  0  0 2X 2X 2X  0  0  0  0  0 2X  0 2X 2X  0  0 2X 2X 2X  0 2X
 0  0  0 2X  0  0 2X 2X  0 2X  0 2X  0 2X 2X 2X  0  0 2X  0 2X 2X 2X 2X  0  0  0  0  0  0 2X  0  0 2X
 0  0  0  0 2X  0 2X  0 2X 2X 2X 2X  0 2X  0  0 2X  0  0 2X 2X  0  0 2X  0  0 2X 2X 2X 2X  0 2X  0  0
 0  0  0  0  0 2X  0 2X 2X 2X  0 2X 2X  0 2X  0 2X  0  0  0  0 2X 2X 2X 2X  0  0 2X  0 2X 2X 2X  0  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+182x^30+128x^31+773x^32+384x^33+1184x^34+384x^35+752x^36+128x^37+164x^38+8x^40+6x^46+2x^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 1.86 seconds.